Travelling during Conditional Green Card

You need to wait for the receipt for filing I 751 which will serve as proof of your extended status.

H1 transfer with Perm approval pending.

I believe you will need to start the process all over again. Consult with an attorney.

Can a i-485 be denied, if I have been deported 29 years ago?

It might not have any consequences, however the reason for the deportation matters and you should consult with an Immigration attorney.

H1B Stamping after Class 1 Misdemeanor in Virginia

You should speak with your lawyer about it, but the main thing: you need to disclose the fact of the charges and present a document showing their...

Green Card with the clerical mistake

You can file a form to replace the incorrectly issued green card. If it is government's mistake, there is no fee for it.

My birth certificate is a problem

You can submit other documents. Talk to an Immigration attorney.

I got LPR thru VAWA. My son was under 21 at the time, but I did not include him in the 360 form. Can he retroactively apply?

All I can say that it will be an issue. You should meet/consult with an attorney. Was your son abused as well?

L1 to H1B

It depends on the timing of all of these changes. Possibly.

Usually not. The only way to be able to travel (and it is very difficult to obtain) is talk to ICE.

Your lawyer will handle this. But just the receipt might not be enough, if A's petition was denied and you were not in a valid status with A before...