What is the oblig. of a U.S. citizen who marries and sponsors an immergrant

He should meet with an immigration attorney to discuss in greater detail but, in essence, divorce does not end the financial aspect of sponsorship.

Who is the best immigration lawyer with a highly successful rate for i-601-i 212?

You can also search for an attorney at aila.org

Can we get US tourist visa for an Indian Citizen who is in UK (in visitor visa for UK)

Yes, this is certainly possible.

I am on an H1B visa. I transferred to a different company. Transfer H1B approved. After a week, I received another offer.

Yes, you can start once the new employer files the H-1B paperwork.

Could be problematic.

How can I show proof of residance? On F1 visa?

I agree with my colleagues.

My kid

I agree with my colleague - you have to prove that you've had a relationship with the child. Meet with an attorney to discuss all that that entails.

Mailing address for work authorization

The I-765 instructions at uscis.gov provide the exact mailing address.

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H4 extension for my dependant but he was arrested last year. What would be the consequence?

Depending on the severity, he may/may not be granted the extension. Meet with an immigration attorney.

Marriage immgration

Meet with an attorney before deciding to skip out on this semester.