Is it possible to play .mid files directly via some API, or one have to convert the midi file to e.g. AAC first?
A:
There is no Apple API for this. You could write your own, which i think would depend on what you are hoping it is going sound like.
There is lots of available source code for reading midi files and there are a few open source synths for the iphone - or you could use openAl for triggering samples. It probably isn't going to sound like Garageband tho.
If you want it to sound as good as possible you will have to convert it first.