Can I transfer my old H1 B from employer A to new employer? Can I be cap exempt?

You would not exempt from the cap given that the original petition was 10 years plus old.

What are our legal options? Should we just not bother trying again for a non-immigrant visa? She doesn't want to go back

You should check to see if she was admitted for 3 or 6 months. Check the passport. If there is a valid explanation and she can indeed show her...

Do I need a new visa? Do I need to get a new I-20 from school and pay sevis fee for new one?

I am sorry for your loss. You should contact the DSO who can go over the specifics.

Is priority date retained when employee change the company after I-140 approval and new employer process fresh PERM and I-140?

You should talk to the new company's immigration attorneys regarding such.

Is " anything " I can do to have my interview here in US ? Or no way to do it?

If you have an attorney please address these questions with them. In general with a 601A waiver (with the situation described above) one does need...

Help needed with marital history questions on citizenship application

see http://www.uscis.gov/sites/default/files/files/form/n-400instr.pdf

As H1B holder, am I eligible for this kind of agreement?

Before signing consult with an employment/contract attorney.

Is there a cance that if I get rejected on student visa my spouse visa would autometically rejected?

See if you are eligible for an f1 visa.

Can I stay back in the US on H4 visa if my wife whose on H1 shifts back to India?

No you cannot. See if you are eligible for an f1 visa.

I would talk to an experienced immigration attorney who can assist you. You can do a search on avvo.