Lainie B

If she is in the US right now, your best course would be to AOS by marrying ASAP, then concurrently filing I-130, I-485, I-765 and I-131. She should have her AP by January if you marry and file right away.
If you do AOS, she can do whatever she wants once she has her green card (school, work, etc).

If she is in the US right now, your best course would be to AOS by marrying ASAP, then concurrently filing I-130, I-485, I-765 and I-131. She should have her AP by January if you marry and file right away.
If you do AOS, she can do whatever she wants once she has her green card (school, work, etc).

You can file right after your wedding. You can even file after his 90 days is up. There is no deadline for filing AOS, you just need to marry within the 90 days, not file within the 90 days. But the sooner you file, the sooner he gets his EAD/AP and eventually green card.

This is incorrect.

This is 100% wrong. Please read the I-9 form. In particular read the "anti-discrimination notice" at the top of the form, and the "list of acceptable documents" at the end.
Employers CANNOT demand to see your green card. You can choose which documents from list A, B and C on the I-9 form. You can show them 1 document from list A (such as a green card or US passport), OR 1 from list B (such as a drivers license) and 1 from list C (such as the SS card without the restriction on it).
Showing your SSN and your drivers license to an employer is not claiming to be a US citizen.

This is 100% wrong. Please read the I-9 form. In particular read the "anti-discrimination notice" at the top of the form, and the "list of acceptable documents" at the end.
Employers CANNOT demand to see your green card. You can choose which documents from list A, B and C on the I-9 form. You can show them 1 document from list A (such as a green card or US passport), OR 1 from list B (such as a drivers license) and 1 from list C (such as the SS card without the restriction on it).
Showing your SSN and your drivers license to an employer is not claiming to be a US citizen.

Which is why, for people transitioning from the EAD or work visa to the green card, as soon as the green card is received it's important to go to the social security office and get a new SS card without the "valid for work only with DHS authorisation" annotation.

Better yet, just show them your social security card (without the "valid only with DHS authorisation" on it) plus your drivers license when you fill out the I-9 form the day you start work, that way you don't even need to show them your green card and extension letter. They cannot demand to see the green card. That way you don't even need to bother explaining your extension letter and pending 10-year card. You are a permanent resident, with the right to live and work in the US, and you don't have to explain anything.

He divorced because he was unable to get a green card through her? And he is in deportation proceedings and you want to marry him so he can possibly get the green card this time? You will have a hard time convincing the USCIS that you have a valid relationship/marriage that is not just for the sole purpose of immigration.
http://www.uscis.gov/laws/immigration-benefits-eoir-removal-proceedings
You need to contact a good immigration attorney for help.

It appears you read this part:
and you neglected to read this part:

Better yet, just show them your social security card (without the "valid only with DHS authorisation" on it) plus your drivers license when you fill out the I-9 form the day you start work, that way you don't even need to show them your green card and extension letter. They cannot demand to see the green card. That way you don't even need to bother explaining your extension letter and pending 10-year card. You are a permanent resident, with the right to live and work in the US, and you don't have to explain anything.

Which is why, for people transitioning from the EAD or work visa to the green card, as soon as the green card is received it's important to go to the social security office and get a new SS card without the "valid for work only with DHS authorisation" annotation.

Which is why, for people transitioning from the EAD or work visa to the green card, as soon as the green card is received it's important to go to the social security office and get a new SS card without the "valid for work only with DHS authorisation" annotation.

It is best to apply for the SSN in maiden name so it matches the name in the system. Some have been able to correctly get the SSN in their married name using their marriage certificate, but many SSA workers don't do things correctly. That is why it is easier to get the SSN in the maiden name and then change it later after getting the EAD in your married name. They want government ID showing your married name in order to change it.
The mistaken part was mainly about choosing the name at the time you marry. Many states do not have you choose and list the new married name anywhere on the license or certificate, so their state might not ask what name they intend to use. They can still use their married name right away and the marriage certificate still acts their legal name change document.

If she is in the US right now, the best option is to stay, marry and adjust status. 4 months is about right, give or take. She would follow this guide: http://www.visajourney.com/content/i130guide2
The other option would take considerably longer (around a year)

If she is in the US right now, the best option is to stay, marry and adjust status. 4 months is about right, give or take. She would follow this guide: http://www.visajourney.com/content/i130guide2
The other option would take considerably longer (around a year)

Whatever name you intend to use from now on should be the one you put on all the AOS forms. That will be the name that appears on your green card. So if you are changing your name to your husband's name, use that on the forms. Don't worry that your passport is still in your maiden name, it doesn't matter. Your marriage certificate is your legal proof of name change.

$420 per I-130 filed.

Whatever name you intend to use from now on should be the one you put on all the AOS forms. That will be the name that appears on your green card. So if you are changing your name to your husband's name, use that on the forms. Don't worry that your passport is still in your maiden name, it doesn't matter. Your marriage certificate is your legal proof of name change.

His extension letter is about to expire, so he can get an extended stamp for another year to wait for i751 decision.

It's a lengthy process, it takes years at immigration court. And it is his problem. You don't have to worry about it. Move on with your life is all you can do.

Aruadha - I have flown into LAX many times, arriving around 6am, and never had to wait for immigration to "open". It's usually been jam-packed, with many big international flights arriving at the same time. Sometimes it takes an hour or two of waiting in line. Perhaps it was so busy that they made you wait for it to clear, or maybe there was something going on at that time, but I can say for certain they do not wait to open at 8am.
Hopeful 4xmas - I understand your question. But there is no difference between your fiancee arriving in the US on the K-1 and every other US citizen/visitor/green card holder/other arrival arriving at the POE. There are different lines for different types of arrivals. Your fiancee will go through immigration inspection just like everyone else. They will most likely take her packet right there, at the entry point where they ask questions and take fingerprints/photos of all arrivals who are not US citizens. Most people on the K-1 are processed within a few minutes. A few are sent to secondary, but it's my impression that's uncommon. There may be a separate line for new immigrants, but it's all in the same inspection area.
However, it is a very good idea to make sure there is enough time to get through immigration and get to the connecting flight, because if it is busy, or she does get pulled into secondary, it can take some time. Allow 2-3 hours, perhaps more depending on the airport.

CBP will be there to accept passengers whenever there is an international arrival, including 5:30am. They will be able to process your fiancee's entry at this hour.

Yes, you can get a SSN, bank account, insurance, gym membership, library card etc etc before the green card. For some of those things you just need to show you are living here, by showing a bill or something with your address on it. If you are getting health insurance through your spouse's work, you should enrol as soon as you get married, as most companies have a one-month period after a "life changing event" (such as marriage) in which you can enrol. Otherwise you will have to wait until the next open enrolment period, or get your own insurance. Once you get the EAD you can work and get a drivers license, even before you receive the green card. In some states you can get the drivers license before you get the EAD, though it is usually a temporary license that expires when the I-94 expires. You are living in the US the minute you step on US soil with the K-1. There are some things that will need to wait until you get the green card, but very few. You should start building your life in the US as soon as you arrive.

CBP will be there to accept passengers whenever there is an international arrival, including 5:30am. They will be able to process your fiancee's entry at this hour.