treppenwitz

She can go alone. But they will allow you to wait in the waiting area if you come.

Just select a few chats. It's recommended to just include about 6 pages.

Just select a few chats. It's recommended to just include about 6 pages.

Not impossible, but highly highly improbable.
 
Below is the published annual report of visas issued. In 2018, there were only 6 K3's issued. Six out of hundreds of thousands of immigrant based visas.
https://travel.state.gov/content/dam/visas/Statistics/AnnualReports/FY2018AnnualReport/FY18AnnualReport - TableXVIB.pdf
 
And you can see in that report that every year the issuance of K3's gets less and less.
 

 
This is why it is often advised on here to not even attempt it. the usual course of action is the K3 gets administratively closed and the case becomes another CR1/IR1.

Correct
Incorrect; green card fee payment info is given out following approval at the interview. 
Important. Mumbai COs could ask to show plans for medical coverage for elderly immigrants as US medical not cheap. 

In the other thread @geowrian said it's possible but very hard:
Especially for a short marriage.
 
To the OP: Below is the relevant part of the USCIS Policy Manual https://www.uscis.gov/policymanual/HTML/PolicyManual-Volume7-PartB-Chapter7.html
 

It seems @Mellamanlola was correct; Cubans that entered legally can still AOS because of the CAA: https://www.uscis.gov/greencard/caa See @Hypnos's post above.

AP granted for any type of AOS can be used for vacation, etc., not only K-1 AOS. AP granted for TPS, etc. limits travel to humanitarian reasons.

Yes it is possible - with a major caveat: it requires the ongoing cooperation of the original petitioner.
They still need to provide an I-864. Given that there is 0 benefit for them to do this, it's not something to expect in the vast majority of cases.
There will also be an AOS interview (a general interview waiver for K-1 no longer exists). No show = expect a denial.
Even with their active support, a 2 month marriage would be an uphill battle. This is lawyer territory IMO.
 
There are people who have done this. But just be aware that it is far out of the norm and the deck will be stacked against you.

You can use AP for a vacation.  
 
It's recommended to be used for short trips because it's always better to prosecute a case from inside the US than when the beneficiary is outside the US.  

Make sure you get the baby's US passport before she leaves the US with the baby.  That process including birth certificate may add a few weeks to your plan.

K-3 is effectively dead - forget that option. It would be marry and file for a CR-1 visa.
 
With either the K-1 or CR-1 option, the petitioner will need to show that you will not become a public charge. This means having income that will continue from the same source upon return to the US. This can be either via them directly or via a co or joint sponsor.
 
The address you use on the application for the mailing address has no bearing on the case except that is where they will mail any notices.
 
That said...
The best option here is almost certainly to marry then do DCF in London for a CR-1 visa. The process will only take a few months, and a CR-1 is superior to a K-1 in nearly every single possible way. The K-1 path has to be filed in the US, which will take the better part of a year from filing to interview.
Once he files the I-130 in London, he can return to the US ahead of you. He will need to show US domicile - or sufficient intent to establish US domicile - before the visa will be issued. Moving first is a good way (but not only way) to do this. A US-based grandparent can be a joint sponsor fine.
 
Edit: Note that DCF is being phased out by the end of the year (supposedly....not confirmed). So the sooner you start, the better.

A stand-alone AP looks like this:

Select "I do not possess any of the documents listed above" and press "Next" Select "Foreign passport, consular identification card, foreign national identification card, or a foreign driver's license. If the foreign driver's license is in a language other than English, it shall be accompanied by a certified translation or an affidavit of translation into English." and press "Next" Select something from the list you have then select "Next"

You can apply. Ask for the AB 60 license. K-1 immigrants can also get this because, according to the CA DMV, K-1s without EADs don't have "satisfactory proof of legal presence"; look at the thread below:
Here is the CA DMV page: https://www.dmv.ca.gov/portal/dmv/detail/ab60

The new I-765 NOA and your current EAD together are the proof of 180 day auto-extension:

Map is outdated.  Texas has a consulate in Houston that covers Arkansas, Louisiana, Mississippi, New Mexico, Oklahoma, and Texas