lost_at_sea

There is literally no more advice anyone can give you that you haven't already received in this thread (have a strong case: a strong case includes lots of evidence of meeting him and his family, photos of you with him and his family, communications via phone, email etc.).
Since you don't want to answer any clarifying questions to make better suggestions to ensure your case goes smoothly, there is no way to help you further. You've had the whole story. This forum is made up of thousands of people, most of which have spent at least some time (if not a lot) thousands of miles away from their partners. with all kinds of weird and wonderful situations. We've seen it all.

I think this thread is one of two things:
1. The OP is not happy to have received some honest advice to make sure that she gets to be with her love by making sure she has a very solid case because of her familial relationship to a person who has previously committed immigration fraud from the same country. Hopefully she will take the advice regardless and she will live the happy life that she wants.
-or-
2. A troll.

*sigh* No one is "naysaying". And photos after the fact don't matter to us - you could have your faces painted on the side of the White House and we'd still only be interested in your application and situation BEFORE that you came here to get help on. We're only interested in helping people to complete their applications correctly and help them through cases with red flags (like yours).
If we were naysaying you'd simply get "He's trying to commit fraud" and no help to build a good case. That's not what's happening.

I am now wondering how far a couple could push the limits of the requirement to have physically met one another - how far apart and how clearly must one be able to see the other? Are you allowed to use binoculars?

There is literally no more advice anyone can give you that you haven't already received in this thread (have a strong case: a strong case includes lots of evidence of meeting him and his family, photos of you with him and his family, communications via phone, email etc.).
Since you don't want to answer any clarifying questions to make better suggestions to ensure your case goes smoothly, there is no way to help you further. You've had the whole story. This forum is made up of thousands of people, most of which have spent at least some time (if not a lot) thousands of miles away from their partners. with all kinds of weird and wonderful situations. We've seen it all.

I am now wondering how far a couple could push the limits of the requirement to have physically met one another - how far apart and how clearly must one be able to see the other? Are you allowed to use binoculars?

You know, I just went back and looked in my calendar, and during the 3 months between my GC expiring and getting my new GC, I didn't actually leave the USA (I travel a bunch, it's easy to forget). I think I would have needed to stop into the GE center to update them with that document for the system not to have got mad at me. I updated them with the new GC when I got that.
So, in short. Ignore me and my use of GE with RoC. Sorry.
Proper order is: Drop into GE office if you need to travel between your 2-year GC expiring and the new one showing up, show them your extension letter and they should extend the GE-OK window. If you're not travelling in that period of time, there's no need to bother - just wait for the 10-year.
When you get the 10 year GC, drop in again and have them update the details.
You don't need to make an appointment to do GE document updates - they do them as walk-ins.
Also, if you don't bother to update your info with GE, the system will just say "invalid details" or whatever and you just do the immigration dance like a non-GE user, so it's not a problem - just means you're back in the slow queue for a while.

Yep, I used GE while doing RoC. When you get a new GC, you need to drop into the GE center and have them update your records.

You only need the extension letter, yes. The border systems don't know anything, even if you had a stamp in your passport, from what I can tell (if they do, they're REALLY good at playing dumb about your status). Do you use nexus or global entry? I've been using GE just fine and used it while my RoC was pending without a stamp and only the letter.
No need to infopass. They'll just want to see your expired GC and the letter at the pre-clearance stop.

So, this form is also used for people applying for tourist visas and they're using that question to understand if the applicant has family there, because that may influence whether the interviewer believes the applicant has immigrant intent.
It's a super general-purpose form and K1s just happen to be a weird non-immigrant applicant type using this form.
As you're all doing K1s, you obviously do have a fianc(e)é in America, but it doesn't matter because you're allowed to have immigrant intent - whether you put yes or no isn't going to affect the outcome (although saying no is weird, since it's at direct odds to the instructions - you'd HOPE K1s have a fianc(e)é or there's going to be some disappointed brides/grooms).

Your case status should say when they've received it (I guess at the moment it tells you they sent you an RFE? That should update when they've got it back in it's right place AFAIK). I'd expect you'll hear something (like NOA2) shortly, as RFE means it was on a real human being's desk being processed.
You could try calling them to see if they have it, but I bet they're as useless at that as everything else.

It's one of two buttons the screen displays. I think most people don't notice, because they're too busy looking down at the scanner, messing with their passports.
Nothing to worry about though - like I say, it's pretty obvious once you see it.

+1 to Penguin. With an endorsed visa (i.e. temp green card), she can turn around at the airport and leave right away again if she wanted to.
SSN has nothing to do with travel.
In regards to Q2, you're correct. To maintain her permanent resident status she needs to be in the USA more than she's out of it.

The vaccinations are *not* required for the K1 (because the K1 is a "non-immigrant" visa), but they are for AOS. The reason people tend to get them at home, particularly if you're somewhere like the UK where you can get them for free from your GP, is because it's a pain-in-the-butt to get them done in the US as you have to find a chartered physician and they're expensive/faff etc. and they may want to do a whole new medical. If you get the vaccinations done during your K1 visa process, they'll supply you with a form that you'll only need to get notarised by the american doctor, instead.
As she's in the UK, she'll be fine at the medical without records. The doctor she'll have to see for the visa medical will be able to offer the vaccines (for a fee) if she doesn't have them and would like them then. I don't have my records at the moment - they're currently lost between two surgeries - but I just got my MMR done (because I knew I hadn't had that one) and if they want me to get the dtap, I'll just have that done at the medical and pay for it. I'm going back to my GP in a couple weeks to see if they've found my records, and if they have and it shows I'm out of date on my dtap, I'll have them do that too.
If she speaks to her GP, she can probably get them done for free. The most they may charge is a prescription for each vaccination (which is like, £7.65 at the moment). I'd really recommend she do them before the medical if it's a money thing, because I'm certain it'll cost you more in the long run if you do them in the US. Take a look at this thread about medicals, btw: http://www.visajourney.com/forums/topic/8321-london-medical-knightsbridge-doctors/
Here's the document about the medical from the London embassy too: http://photos.state.gov/libraries/unitedkingdom/164203/cons-visa/iv018a_medical.pdf
See:
"Special notice for K visa applicants: K visa applicants are not required to meet the
vaccination requirements at the time they apply for a visa. However, they are required to
meet them at the time they apply for an adjustment of status in the United States. If you
take your vaccination records to the medical appointment, it may be possible to use the
results of the medical examination in the United States."

Affidavits really aren't necessary unless you don't have any primary evidence (financial, co-mingled assets, proof of living together). There's no need to hassle your friends and family.  I don't want people to think that they're necessary - we sent 0. We sent zero photos, plane tickets etc. 
 
 

I still have an ISA from before I moved in the UK. I just left it there, and we take a bit out of it now and then when we go to the UK to save on conversion fees / emergency money when abroad.  If you want to leave it there, as Wuozopo says, you just need to declare it every year if it's above a certain amount in value.
 
It's called FBAR: https://www.irs.gov/businesses/small-businesses-self-employed/report-of-foreign-bank-and-financial-accounts-fbar
 
It used to be higher than 10k, but I see the number has been reduced. Annoying.

Affidavits really aren't necessary unless you don't have any primary evidence (financial, co-mingled assets, proof of living together). There's no need to hassle your friends and family.  I don't want people to think that they're necessary - we sent 0. We sent zero photos, plane tickets etc. 
 
 

If you keep a foreign financial account while living in the US, you have to remember to file a disclosure report of it to the US Treasury each year that balance exceeds $10k. It's online and easy. It used to be due in June but  this year moved to April for reporting 2016.  If you earn interest/dividends on your foreign account, the earnings for the year are reportable on your tax return as income. The whole balance is not taxed, nor is there any US tax obligation if you transfer the money to the US, except for yearly interest you may earn. I use Transferwise to move money from the UK.

Did my oath today in Oakland, California. All done! Woop. 
 
There were 1232 people being sworn in from 91 countries at my ceremony today.
 
 
--
 
 
 
There's no drawback, other than the delay in time. I expect they get a lot of requests for reschedules over the summer holidays.

The quote thing doesn't seem to work really in the new updated version of the site. It's actually easier to simply copy and paste it.  I updated the instructions, but I'll copy it out again.

The requirement to show that you had met in the 2 years prior is pretty key to the application, so I'm not surprised you got RFEd for that. I think what you're sending now should do the trick (namely the passport stamps, boarding passes and photos together).  
 
In terms of "Where did we go wrong the first time?", if you didn't send them any evidence that you'd met face-to-face in your first package to satisfy the "met in the 2 years prior" rule, then that's where you went wrong. No biggy, just slowed things down a tad.  
 
Photos aren't evidence of the "2 year" part (they are evidence of meeting, but not WHEN) and neither are letters etc. Buying plane tickets doesn't mean you got on the plane, could be faked.
 
Basically, you have to put your suspicious hat on and think to yourself "what evidence would be difficult for someone to produce if they were faking it".  
 
The passport stamps are government issued items, so they're really good. That, coupled with some evidence of your activity while there (that receipt, for example) makes it a lot easier for them to tick the "yes they met with in the last 2 years" box.

As somebody who works in IT, I'm doubtful they would treat it much differently from a normally-printed photo. Geotagging and date stamps are very easily and quickly modifiable without a trace. You can change the date taken in Windows right from the right-click -> Properties menu. Changing the GPS attributes need other (easily obtainable) software, but somebody actually committing fraud would have no trouble doing it. Somebody committing fraud could do a lot with photos (part of the reason why they are secondary evidence only), but changing EXIF data would be probably the easiest to do and hardest to detect.

The requirement to show that you had met in the 2 years prior is pretty key to the application, so I'm not surprised you got RFEd for that. I think what you're sending now should do the trick (namely the passport stamps, boarding passes and photos together).  
 
In terms of "Where did we go wrong the first time?", if you didn't send them any evidence that you'd met face-to-face in your first package to satisfy the "met in the 2 years prior" rule, then that's where you went wrong. No biggy, just slowed things down a tad.  
 
Photos aren't evidence of the "2 year" part (they are evidence of meeting, but not WHEN) and neither are letters etc. Buying plane tickets doesn't mean you got on the plane, could be faked.
 
Basically, you have to put your suspicious hat on and think to yourself "what evidence would be difficult for someone to produce if they were faking it".  
 
The passport stamps are government issued items, so they're really good. That, coupled with some evidence of your activity while there (that receipt, for example) makes it a lot easier for them to tick the "yes they met with in the last 2 years" box.

I updated my comment a little after. Sorry.
 
Anyway. This is me playing officer again and imagining how they might scrutinise.  The Tower of London photo - that could have been taken any time, not necessarily on that trip. It shows you met, but doesn't prove the when.
 
Having the passport stamps is important because they're government issued, so in their eyes, less likely to be faked.  Travel itineraries are documents made by private companies that they can't verify. 
 
It's a combination of things.  They want hard stuff (government issued things, for example) with corroborating secondary stuff (like boarding passes). They use them all together to form an idea of how likely it is that you actually met the criteria that they can't possibly really, truly, know (without a time machine or having personally met you both at the same time on that trip). 

You appear to be in filing for a K1 in Australia, so your embassy should accept a joint sponsor. A joint sponsor can be anyone over 18, resident in the USA, an LPR or citizen and have the required amount of money.
 
I recommend you read the I-864 and accompanying instructions.  https://www.uscis.gov/i-864
 
You'll be supplying the I-134* for the K1 process, but the embassies follow roughly the same rules as for the I-864, which you'll be completing during the AoS procedure anyway and will need the same financial information, except more stringently. 
 
The Australian's income does not count because it will not continue in the USA.  Savings/assets can count, so if you happen to have a lot that's also an option. 
 
* https://www.uscis.gov/i-134