Is the 10 year immigration law true?

It is true but you cannot apply if you were previously deported. As you took voluntary departure before, I am assuming this was in removal...

I entry to US in 2005 with a B-1, and get married with a cuban, he had residence in 1980 and in 1986 his residence expired

To answer we need to have exact Information. This is too vague to tell us what really happened.

I have a greencard (marriage) but have accepted job in home country. Can I keep my greencard in case I want to come back to USA?

You should apply for a re-entry permit which will allow you to remain outside for up to two years.

Can we file for a Waiver of Excludability?

You need to take all your facts and let an attorney look at everything you have. We are not even sure what he was convicted of.

What do we need to do in this case?

Oh boy - first of all - you are assuming a lot. If I were the person in jail, I would not want my case to be "assumed" but handled. You need to...

Is there federal help for Filipinos who are Naturalized US citizens?

Not an immigration question but try for an SBA loan if she is a citizen. They like minorities I hear.

If someone falsely claimed to be a US citizen

For kids there is a special exception where they have USC parents and all along thought they were USC's living in the US...

Is it true that if someone falsely claimed US citizenship at the border before 1996

If before 1996? Yes - there was no permanent bar until the law changed.........

G 325-A Form - Spousal Visa Employment Records

You have to be honest on the form and put what he does on it. Hopefully he has been paying some taxes on his cash income, as that is the law. ...

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What sort of adjustment of status or immigration benefit is available to the parents of a newly borned u.s citizen child

Unfortunately for you - nothing.