thank you for your question in the community.
As for your question:
1. to Marry in italy without providing your Passport and the Certificate of Nulla Osta (Certificate of no impediment) it is impossible, so you need to have these documents;
2. your girlfriend as an American has to come to Italy to get married and getall her papers from America certified;
3. after got married your girlfriend ahs to apply for an family unifiaction at the american authorities.
I hope this could help answer some parts of your questions, if you need further assistance please do not hesitate to contact us.