With regards to your last question, U.S. citizens can go and live abroad without giving up their citizenship.
There may be ways that you can help him legalize his status once you marry, but it depends on a number of factors, and you should definitely consult an attorney. For example, I'm not sure when you say that he "got in trouble when he was younger," whether you mean that he has only a juvenile record, which carries fewer immigration consequences. Also, it's not clear what you mean by "sentenced to 10 years no re-entry." It seems like he was barred from re-entry by immigration, possibly because of previously accrued unlawful presence, but it's really not clear from what you state above. You should consult an immigration attorney.
For general information, you should visit www.uscis.gov. The process depends on the details of your fiancee's immigration and criminal history. His case seems to have some issues. You should see an attorney. Watch out for common immigration scams and make sure you see a licensed attorney who specializes in immigration.
Please note that this response for informational purposes only and does not create an attorney-client relationship.
Same way you would marry him if he was a USC.
The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter,not should it be viewed as establishing an attorney client relationship of any kind.