You can get a new birth certificate, or she could get a new birth certificate, marriage certificate and passport.

If you have a pending application for H4 extension, and you leave, CIS will deny that application.

If your spouse does not want you to know about the case, she can easily change the I-751 to request removal of condition under a category other...

Could be. There is no way to know. But since it was current last year, and there are so few visas being issued, it is likely it will remain...

If you cannot work for the petitioning employer, it's not a problem. But if you can and you choose not to, it could be a problem.

You can certainly show up on the date listed. You should expect that you will not be interviewed on that date.

I do not see the benefit to showing up to a cancelled interview.

If she has a green card, she can use it to work and to travel into and out of the U.S.

If there was a forgery it will be a problem. And if not it will not.

If CIS approves your I-485, you will get a green card.