No, your wife cannot have you deported if you are a lawful permanent resident.
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Hello, it is possible that he might be eligible for the new Deferred Action Program for young people. I would be happy to meet with you and see if he is eligible for the program. You can call my office at (520) 624-3400. Siovhan Sheridan
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You can either get proof of your citizenship through the Immigration Agency, but filing for a certificate of citizenship, or you can apply for a U.S. passport through the Department of State. There are ways to prove your birth in the U.S. without a registered birth certificate. For example, affidavits from people who were present at your birth can also be acceptable with other proof. I would suggest hiring an attorney for help with the process.
It could be possible for you the get your greencard through you new marriage. Given your history, I would recommend using an immigration attorney during the process.