Hi my husband and I just recently got married he is German citizen and I am American citizen....He's a student

Ok so here's the deal he has been here for 8mos or so...I just got back from Iraq was in the Army when we met in Stuttgart 2yrs ago..Anyway how long does this process take and do we need to start any paperwork so that we don't have to renew his student visa which is really expensive? Also does it matter that my current address is in Northern California and his is So. Cal? I mean do we have to use one single address? I just want to make sure we get most of this done soon cuz' I deploy to Kuwait in about a wk or so we just got married on the 15th of Jan...also do I need to change my last name to his to show validity of our marriage in this process??? Lots of questions I know...plus he's he's half German half Iranian will that have any bearing on this process, I mean should he just skip the Iranian part? I mean on the marriage license it shows his dad is from Germany and his mom is from Iran...Pls help I'm 26 & he's 29 so we want to make sure everything goes well...thanks