Can I get US residency through my mentally and physically daughter who is a minor US citizen?

Both attorneys are correct: (1) court is an option, but you need to get arrested ... not a good idea (2) your son/daughter can file paper, but...

Male on h4 is thrown out of house from his wife who is on H1B and left on his own. Can he file for work permit ?

This is a long and complicated story ... you should tell it to an attorney in person. Normally an H-4 can not get a work permit.

Can someone who filed a 360form in April apply for an A visa while the application is still pending?

As my colleague stated, you didn't give enough facts. This is a complicated area ... talk to an attorney before filing more papers and/or leaving...

Can i keep getting multiple 3 yrs h1b extensions based on ex-employer's I-140 without current employer restarting GC process.

You are proposing a very complicated strategy. Talk to a lawyer.

What is the next step for approved I130, IMMIGRANT PETITION FOR RELATIVE, FIANCE(E), OR ORPHAN?

Talk to a lawyer ... you are probably on a waiting list that could be several years long. Talk to a lawyer about your parent becoming a US citizen.

It is a bit complicated. But, you should be OK: http://travel.state.gov/visa/temp/info/info_1299.html

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Am I allowed to travel out and get back in US normally if My US naturalization was denied?

You should be ok. It appears that you filed for naturalization when you weren't eligible ... nothing more.

Deny my I-751

GET A LAWYER before you do anything more.

Can a legal resident alien go out of the country and come back whit a misdemeanor

Follow the advice of the three lawyers ... apply for US citizenship before leaving the US ... that is the safest/best way to proceed.

Can my mom change status or get an EAD?

As the other attorney stated, filing an 'employer petition' before the I-94 expired is NOT the same as filing an application for extension of...