Cuban fiance was in jail for Peligrosidad in Cuba. Could that affect our K-1 visa application?

It might have an impact. But since he was likely a politcal prisoner, it should be a deal breaker. Cuba is a totalitarian regime it imprisons...

What matters if i marry a SO in US if a have a tourist visa now?

You will have to work around the Adam Walsh Act. This is something you need to coordinate with an attorney. You may be eligible for a waiver.

Can i file US citizenship?

You can file at the 4 years and 9 months mark. The good thing about waiting 5 years is that you need to use less information regarding your spouse.

The violation of the Walsh Act may present a problem. As the others have suggested, you will likely need to file a waiver in this situation. You...

In applying for spousal green card, is it necessary to submit exact dates of entry to the US?

The last I-94 is what is most important. You may have to disclose prior visas held as well.

Do I need a waiver to apply for a green card if I overstayed?

Since you entered legally and then overstayed, marrying a US citizen will be sufficient. You will not need to request an unlawful presence waiver.

How can I obtain work permit and SSN if I come by tourist visa?

A tourist visa is just a short term visitor visa (up to 6 months at a time). After a few months you have to go home. You have no right gain a...

Can the baby born to an out of status mother and in status father obtain a SSN and passport to travel to parents home country?

It would depend upon where the child was born. If born in the USA the baby will be an American citizen and eligible for all of those things. ...

How will my expired US visa be cured? Is it through marriage? My fiancè is an American citizen.

Your visa might be cured if you get married. It depends on the situation. I would need more information before commenting in more detail.

Im a residence in us ?

You will have to wait until you are a citizen before applying for her green card. ...