Questions about applying for a Work Visa (Munich)

Hi there,

I live in the US and have decided to take an unpaid internship in Munich and wanted to apply for a Work Visa before I get to there. I have a couple of concerns and questions regarding the whole process.

1- I, semi have a place to stay, but it's not a definite place since my internship will only go on for 3 months and the commute will be longer than actually staying in the city. Would it be a problem if I wrote the address I'm going to, but change my address if I find an apartment closer to the internship?

2- I can get a letter of intent from the internship to make the application process smoother but would it matter that it's not paid?

3- Would it be a problem if they sent the letter of intent and then I could apply for a job that pays so I can work part time and not starve while I'm there?

4- Lastly, if anyone has any advice on how to proceed with this, I'm really confused and need some help/advice.

Hope my questions weren't too dumb. Thanks,

Nesli