Am I eligible for US citizenship or not?

You were out of the US for a period of eight months during the five years prior to applying for citizenship. That eight month absence broke your...

Can my girlfriend get a green card if i marry her in case if i win my political asylum case based on my sexual orientation?

Your spouse may get asylum if you get married before a decision is rendered in your asylum case. She will be eligible for a green card one year later.

Can I incorporate in USA as immigrant? What document do i need?

This is not an immigration question. You should go to a corporations attorney,

Do I qualify for adjusment of status if I overstayed and if my 1539 change of status was denied? Is all hope lost?

It depends on who is petitioning for you. If you are the beneficiary of an immediate relative petition, being out of status will not be a problem....

Under section 9 of the INA Amendments of 1976 (Public Law 94-571), an alien who was registered as a Western Hemisphere immigrant with a priority...

Could I take my kid after the issuance of IV for my wife?

Yes, you have it right. If the child is born in the sequence you described, the child will not need a visa.

Of course, you can't work in the US outside your H1B but no problem in another country, as long as it does not entail performing any work in the US.

My sis is a US citizen . I have a F1 visa. Can she file for me to get a greencard while I am in the US on vacation for 6 months?

It would take at least twelve years for the petition, which would be F4, to have a current priority date, allowing you then to apply for a visa.

How to recover your lost foreign national passport while in the united states

Make a police report and got to your country's consulate for a new passport.

It could take several months. You need to call customer service.