Permanent resident card

No. You can move.

Are there any implication of leaving US and residing in an another country for 5 years right after obtaining US Citizenship?

As a US citizen there are no restrictions of time spent outside of the US. You keep your citizenship until you decide to renounce.

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Whats multipurpose petition?

Do not know what you are talking about.

Can i do finger prints from a different state incase my appoint comes up when am away from my state?

I agree with my colleague.

My husban is detained with ice currently fighting his case can he?

Need more facts.

Testifying in court room soon. Under oath what should I answer if my immigration status comes up? Do I need a lawyer for this?

You cannot get arrested it is beyond the criminal court's jurisdiction. You have to tell the truth when you testify under oath. Your immigration...

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I came to the USA with what looks to be a B1/B2 visa type, should I put that under Manner of last entre?

B1-B2/Visitor is fine.

What does <<<<< these symbols mean on the back of the green card?

Nothing really. They are used to separate the numbers, letters.

What happens to a pending immigration case after 3 years of marriage to a us citizen that no longer wants to be together?

If you get divorced before you get a decision in your case, it will be denied. You will not longer be entitled to the benefit.

Would I be able to apply for student visa to the USA after being deported and getting a 10 year ban?

I agree with my colleague. You may even be able to apply for a nonimmigrant waiver.