A green card holder may be active in a political party that does not require US citizenship, but must not vote.

the filing of an immigrant petition is not a problem for H and L visa holders that allows immigrant intent.

I94 expired one month before the H1 extension filed date.

You were out of status at the time of filing the H extension. Premium process urgently advised. Must depart the US before your 180 days of out...

Is it safe to travel outside US and enter US based on AP given the situation or will there be a problem due to expired I94.

Advance parole is generally permissible for travel and travel may be advised where a person has filed an adjustment of status when filed...

Wife changed her name to maiden and I am applying soon for citizenship

Your N400 supporting documentation will support your explanation

Non immigrant visa holder

I cannot make out what you are meaning.

Can I leave my J-1 employer?

a program sponsor will need to approve a move.

Do the E2 Employer and Employee have to be of the same citizenship or nationality?

Both France and Jordan are E treat countries. You may seek companies owned by either. You might work in as an essential specialized knowledge...

Why do I get detain at the US immigration at the airport for background clearance every time I return from abroad?

from your statement it seems they need to confirm your identity.

Does total years of experience with petitioning employer matter in case of L1A ?

the L1A requires employment abroad for at least 1 year as an executive or manager or specialized knowledge employee to be transferred to a related...