Rose711

The information on the website of the U.S. Embassy in Lebanon is different from the usual K-1 process. I think that it would be better if you or your fiancé(e) contacted the U.S. Embassy in Lebanon.
 
Perhaps there are more pertinent information in the regional forum:
https://www.visajourney.com/forums/forum/97-middle-east-and-north-africa/.

You might want to check the guides section here on VJ.....seems you have a lot more to learn about the process.  
https://www.visajourney.com/content/k1guide/
https://www.visajourney.com/content/k1flow/
https://www.visajourney.com/content/k1tips/

Who sends in an unsigned lease agreement and doesn’t even live there?
Who tells an IO that a family wedding celebration was held but no family was there?
Who signs an affidavit of a relationship and never laid eyes on the other spouse?
 
Truthfully, I feel you are very lucky to not have been hit with a misrep.     
 
There is so much fabrication here that I doubt appeal is possible.  Your lawyer is incompetent if he/she filed this garbage.  I’d plan to build a real marriage, refile, and start over.  

You are comparing apples and oranges.  Marriage-based visas from MENA countries are not nearly as easily had as those from Australia.

The evidence has to be taken in context too. We also had no family at the wedding. It was a courthouse ceremony that lasted all of 8 minutes (we walked in at 11 am and we have a photo taken of us holding the ceremonial marriage certificate under a clock that is displaying 11:08 - that’s how we know how quick it was) with just us, two witnesses as required by state law, and the officiant. One of the witnesses was not even related to either of us, just a friend of my husband’s. However, for a British woman who has been married and divorced before (which I have) a small simple ceremony is quite normal for the second marriage. Not one of my family attended. My mother didn’t even know we had got married until the next day. We had been married for 3 years before either of my parents even met my husband. 
 
For a Muslim man’s first marriage, this would be unusual. Big, traditional weddings are far more commonplace in their culture, as well as heavy family involvement. Eloping is not typical there. 

No,  not for you but in  muslim countries,  it is extremely important to show the muslim mother approves of the marriage 
my mom could not be in Morocco (arthritis makes it impossble for her to travel and use the hole instead of a tiolet) iand my mother in law was in the hospital when we were called to come sign the marriage certificate which meant we were married but we had proof in many other photos that she was with us for my visits and i stayed in her home.   very very important for a muslim.
 

You realize that each consulate will be able to see all of your applications / denials.   Consulate shopping does not end well.
 
 
Was there a reason that your VIsa was denied? 

ESTA allows you up to 90 days per entry at CBP's discretion, not sure what you mean by "still allowed to stay for a week".
 
You think you have 90 days per year on ESTA, don't you? And you stayed pretty close to 90 days twice. This is incorrect, you have 90 days per entry at CBP discretion. Sounds like you're trying to spend too much time in the US on ESTA. What do you do for work that you get so much vacation? What are your ties to your home country?
Also, tourism visas are B2.
 
ESTA allows 90 days per entry maximum, not 180.
You can no longer use your current ESTA, must reapply after a material change.
 
 
Good luck.

I agree. This is a lot of time to spend in the US, and I think showing up at the POE saying I am only going to stay the 5 days I have left on my ESTA is not going to wash with the CBP. Why would someone come all this way for 5 days unless for a business meeting or something. They are going to see last spent 85 days, then spend 88 days ( Both visits taking it to the max) and now only 5 days. I think you will got a do not pass go, do not collect 200 dollars on the next attempt to enter, but I could be wrong.

As a practical matter, how many ESTA visas get approved after a B1/2 denial? I’ve  heard that a denial for another visa means that ESTA won’t be granted. Please correct me if I’m wrong.
 
This is my reference:
https://help.cbp.gov/app/answers/detail/a_id/1097/~/previously-denied-a-visa-or-immigration-benefit

Per visa reciprocity, max b1/2 visa issuance is 12 months for Iraqi citizens. So she wouldn’t be able to get longer duration visa. 
All info on travel.state.gov or search visa reciprocity Iraq. 

Why are you trying to spend so much time here?  They may think you're trying to live in the US as a tourist.

As a practical matter, how many ESTA visas get approved after a B1/2 denial? I’ve  heard that a denial for another visa means that ESTA won’t be granted. Please correct me if I’m wrong.
 
This is my reference:
https://help.cbp.gov/app/answers/detail/a_id/1097/~/previously-denied-a-visa-or-immigration-benefit

It's rare. https://www.tripadvisor.com/ShowTopic-g1-i10702-k9156057-My_ESTA_approved_after_being_refused_a_US_visa-Air_Travel.html He answered "yes" to being denied a visa.

One of the biggest educational chasms in the U.S. is the seemingly universal lack of knowledge about legal immigration.
We're very lucky to be regulars on VJ.

To put it bluntly, your marriage seems like(removed) and the USCIS called you out on it. It's applications like yours that slow down the system for everyone else. Deserved denial, an appeal won't help unless and until you have a bona fide marriage, where you know, family actually attends your wedding and you have real conversations not made up ones. 

Thanks for posting the actual notice.  I have copied this NOIR for future reference.  

I think a lot more information on the timeline of the relationship, how often and how long you saw each other in person (both before filing the I-130 and afterwards), etc. would be helpful here.
There does appear to be a couple red flags, which would increase scrutiny of the relationship. Besides the age and religion gap, are there any otgher red flags (short time together before getting married, or doing so on the first visit?) No way to avoid those, but it can be overcome with enough relationship evidence. Time spent in person is the best evidence.
 
A lot of the reasons provided in the denial refer to providing documentation for the sake of having documentation, not of showing an actual bona fide relationship.
Can you provide a full list of:
1) What was provided with the I-130?
2) What was provided at NVC and/or the consulate interview?
3) What was provided in the response to the NOIR?
 
According to the denial, it sounds like the majority of the evidence provided was from friends and family, unverifiable sources, which held no weight.
Can you explain the wedding situation a little more? It states that the wedding was an event for the family, but there were no photos with them provided and the beneficiary did not explain why they were not in attendance. Is that accurate - were they not there?
 
Moving forward, it doesn't sound like an appeal makes much sense unless you can show they made a mistake or have other evidence - from prior to filing - that was not previously submitted. It appears that the best thing is to get more time together in person, gather plenty of evidence, and then file again with a well prepared packet.
Option 2 is to migrate in the other direction. Even if it's just temporary. Although I do understand the challenges in doing so when she has 2 children...it just might not be feasible but it is worth mentioning.