Your prior marriages will not affect your application if you never applied for status. Your fiance's conviction should not affect your application, either unless it is for sexual assault or endangering the welfare of a child. Her divorce could have some influence depending on the timing and if she ever sponsored someone else for a green card. In short, you need to consult with a lawyer to review the details before taking any action.
If she is a citizen and you get married, she can file an I-130 petition for you. There may be other ways for you to obtain permanent residence in the U.S., but you would need to consult an immigration lawyer to determine all of your options.
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Yes, she can file sponsorship papers.
If you're not legally in the US, or didn't last enter the US with a valid visa ... you'll probably need a waiver.
Meet with a lawyer.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
UNless he felony has to do with sexual abuse of a minor or violence against previous spouse, and/or you have barged into this country via border without being inspected or came on one fo those restricted visas, yes, you can.
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Your previous marriages will not matter if you never applied for immigration benefits through them. Hopefully you can show divorces for each. If you marry your current GF and she petitions you, you can then obtain a GC. The fact that she has a felony on her record should have no effect on her ability to sponsor you, unless the felony was for a sexual crime involving a minor.
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
The facts you describe will not prevent your acquiring a green card. However, as my colleagues have stated more information needs to be reviewed before you rely on an answer here.
973-984-0800. Please be advised my answers to questions does not constitute legal advise and you should not rely on it, due to the fact that we have never met, I have not been aprised of the facts in you case nor have I reviewed any documents.