I don't want to go into how I got the visa, but I will say that most people get friends with German companies (even single person companies) to write contracts for them :) The contract simply has to state the project, date of future employment, and how much you will be paid upon completion.

The contract can be for future dates. Does not need to be a project that is currently paying you.

I had one German company and one US company. I think it's safer to have at least one German company.

Sure thing, contact me if you need advice. I haven't been through the process in a couple of years but expats talk about it a lot.