Any issues with H1B transfer and notice with receipt notice

If the application is not approved you will not be permitted to remain

Petitioning step child...

The child will need a release from the mother.

Can I reapply for a green card through marriage with USA green card holder after surrendered my green card 12 yrs back?

Yes it is possible, you may have some explaining as to the past abandonment.

I'm in the process of renewing my green card(exp aug 2017), should I travel or wait until I get my new green card?

Travel is okay. You need a valid passport and visa (resident card).

I'm in the process of renewing my green card(exp aug 2017), should I travel or wait until I get my new green card?

travel is okay. You are required to have a valid passport and visa (resident card).

You should check with SSA as the reason for the delay. Yes you may try to have your name corrected with USCIS.

Contact an immigration or fully read up on the U visa. Does not appear you are eligible from the information you have provide.

AOS or Consular Processing

You have many decisions and you need to make the best choice. To fully understand your options and consequences meet with an immigration attorney.

I-130: After filing just received a I-797C receipt from USCIS

If eligible to adjust the I-30 and I-485 may be filed concurrently

Does getting housing assistance affect my husband adjusting his status?

means tested benefits will likely pose and issue.