If you do not maintain F1 status, and instead you get TPS and TPS ends, you will not be in legal status.

You may never get them back. There used to be a form to request CIS to return original documents, and perhaps there still is, but you should be...

If your foreign passport is not expired, you may be able to use it, but it may be better to file for a reentry permit.

Perhaps there is something missing but generally DHS is not interested in whether an employer overpaid taxes.

Third preference family based is now at December 8 of 2008 so over 15 years.

I don't see why you could not do that since you are including the child in your household size.

Fiance petition is fastest way to get her here.

It could be an issue. I suggest providing an I-134 instead to avoid problems.

Indicate that the green card has mistakes on your name and date of birth.

From 7 days to 10 years, in all seriousness. Yes you should file N-400.