Hi Im getting married and when i went to get my marrige licence i took of one of last names and kept only my miaden?

Your question is unclear. Please repost with clear and correct language.

Does it work if my wife uses my marriage certificate to establish marriage relationship to me for her application?

As long as same date and place of birth and logically similar name, should work.

My husband is a US citizen, Can he apply GC for my parents? How long will it for my parents to get their GC?

That's correct. There is no visa category for one's parents in-law.

Working with an experienced lawyer is the right thing to do if you want certainty and peace of mind.

Currently working on H1-B for X company and I got an intern offer from company B ?

I agree. Cannot "intern" for any other employer unless that employer first files its own H-1B petiton on your behalf.

The Asylum interview schedule at different states are different , does these effect?

I agree. Don't do it; you will likely be sorry if you did.

That's correct. Any good asylum lawyer in your city will know how to proceed with a Nunc Pro Tunc application.

How should I proceed to get overdue unpaid child support for my child.

Your sole remedy under the circumstances is to pursue this with an Austrian family law attorney.

What is the best thing to do in our situation? (Regarding H1b)

I agree. It is best to travel on H-1B, then reenter on H-1B and apply for AOS at a later date, once back in the US on H-1B status.

Do I need to bring my wife to I-485 (as a derivative asylee) interview?

I would recommend bringing your wife with you to the interview. Better be safe than sorry.