1. This is solely up to you and your fiancé. You could marry and file now or complete your studies and marry.
2. You could travel with advance parole. Advance parole can be requested as part of the adjustment of status process. If granted, you could travel outside the United States.
You can read more about adjustment of status at http://myattorneyusa.com/adjustment-of-immigration-status.
Answered on Jun 13th, 2016 at 4:15 AM