I would consider trying to get a DAAD scholarship or something like that - instead of taking out a loan. Just a question, do you really want to get a loan in dollars and then have to convert that to euros?!?!?! Would highly recommend scholarships - there are quite a few for Americans if you have never lived in Germany, or if you've only been here a short time.
I am not sure about DAAD schloraships, but some do not "allow" you to earn additional money - just an FYI. I would check into DAAD's regulations. DAAD is not going to give you money if you study anywhere else, however, you will find that almost every city in Germany is cheaper than Munich. So you could stretch your stipend a bit more. Some scholarships will add a bit more if you live in an expensive city.
Also, as a master's student, I am not sure how long you can live in the student dorms. I believe it is limited to one or two semesters. I would try a WG - especially if you want to improve your German.
www.vierwaen.de or
www.studenten-wg.de - sorry only in German
You can get health insurance without an problems, and really cheap, if you are a student. Not sure about TU, but LMU requires you to have German health insurance before you are allowed to register as a student. I only paid about 60 Euros a month - very cheap! I would wait to get the health insurance until you are accepted - the health insurance requires proof that you have been accepted. Apply for the visa after you've been accepted - because they will also require proof that you've been accepted. You can get the visa after you are in Munich.
If you are looking into taking intensive German courses, they are going to cost you. The unis offer German courses, but I found them to be disappointing - probably because I had foreigners teaching some of my courses! But to start, it might not be such a bad thing :-)
If you want more info on housing, uni system, or scholarships, etc. you can pm me. I studied in Munich and am now at another uni in Germany. Have had plenty of experience with German unis. Best of luck!