I got my permanent Gr.Card for 10 years.Me and my husband are divorcing. Is it necessary to change my last name on Gr.Card?

Typically courts allow for a person to change their name as part of the divorce decree. You will have to advise immigration of the change.

File a complaint with the US Labor department as well as the Illinois Labor Department.

If I have a DUI and have plans to travel to my home in Asia, can I transit via Germany/ UK/ Dubai/Abu Dhabi ?

Because this is a US immigration forum, you would need to address a legal forum in those countries. Sorry.

I would like to apply for I-130 for adopted child whom I didn't see for 19 years, can I?

For immigration purposes among other things the adoption has to take place before age 16. On that basis you cannot apply for her.

I have pending I130 & now i'm in states with B1 visa.can apply for asylum ? Or I will loose my I130 case ???

You can have both pending at the same time. You cannot adjust status now based on your facts.

How long does I-601 take?

It depends on how long it takes you to produce enough evidence to prove extreme hardship to the qualifying relative. No easy task. Once it is...

My H1B visa amendment is in process. Can i raise a dependent visa on i797(notice)?

It is necessary to get the H1B visa first.

There are no restrictions to getting married because of your Q1 visa.

Yes you can but I find that a pencil is best.

I'm on H1 and decided to put investment in a US start up company by taking certain percentage of equity . any restrictions ?

No restrictions on receiving passive income.