Should a Cuban national that arrived in the U.S. in 1966 file a I-485 under "Registry" or the "Native of Cuba" type?

You are eligible for both benefits, but Cuban Adjustment is probably easier.

Do I need police clearance for adjustment of status or Fingerprint at USCIS is enough?

You do need records from your arrest in India, but you do not need any police clearance to file for adjustment of status.

Can i get married and then take my parentes if both are mexicans?, i am an american citizen

You can apply for your parents to immigrate, and you can apply for your boyfriend [if you marry him] to immigrate to the U.S. You can file either...

How long does I130, IMMIGRANT PETITION FOR RELATIVE, FIANCE(E), OR ORPHAN take?

It takes about a year.

I'm an H4 visa holder. Is it legal to apply for a job opening in India and work online? I would be paid in India.

There is always some risk since unauthorized employment is not defined.

Can I file a petition for my Husband whilst living and working outside of the US?

You lack the residency requirement for the affidavit of support and perhaps you should consider filing for a K3.

Either way is fine.

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H1B Question with Prime Vendor as employer

It seems to me that if the employer does not terminate you, you will be in status even when the project is over [and they will need to pay your...

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Change of status from F1 to H1.

If you are no longer an H1b, I do not see how you can get an H1b extension.

Is the process of getting the permanent greed card will b unvalid if couple cancel the marriage contract of the church ?

A green card is valid even after a divorce, whether it is a religious divorce, or a civil divorce.