MY FIANCE SIGNED A VOLUTARY DEPORTATION ABOUT 2 YEARS AGO HOW CAN I FIND OUT IF HE HAS A PUNSHIMENT TIME?

See my other answer.

Citizenship

No, you must live together or you will be denied.

How do I explain to USCIS why my wife and I haven't resided together since I received my green card?

You can certainly try but getting approved is not easy and you will definitely have to have an interview.

Can my us citizen brother petition for me in a new petition

I agree with my colleagues, new petition new priority date.

How can my fiancée get a green card?

After married, you can petition him and unless he falls under an exception, he may have to complete his case in his home country.

? immigration

You really need to disucss with an experienced lawyer. 3 times is not a good thing. You may be denied on discretion.

I am a US citizen and will marry my girl friend who is holding a F-1 visa that expires soon. Once married what do i need to do?

Yes she should be able to stay. You must file all the proper documents, pay the fees etc...

No, not considered a legal marriage in the US for immigration purposes.

Child Status

Yes, even with a us citizen child you can be deported.

I need a Immigration Attorney to help me with an Issue, Haitian TPS?

The abuse case seems more possible but the best thing is to find an immigration lawyer to review all your options.