I'm a musician/composer and would like to record the songs I
have that come into my computer from an external source,
my sound card or mixer.
Will I be able to record my own songs? Will the recordings
be in .wav or mp3 files format? Can I change the recording
setting like higher vs lower quality?
Sounds like you just need Audacity? Otherwise buy the Samplitude Studio which will give you a wide range of possibilities e.g. wav, mp3, direct podcast export ... etc. - I don't know about Music Maker, so others will have to answer that.
You need an external input in your soundcard or a small mixer og direct input to your onboard soundcard. Don't use two soundcards or use the ASIO4All, where you easily can switch off each soundcard.
If it's just to try things out, I record songs on my Sonyericsson and use the recordings in my computer as wav-files, other phones can probably do the same.