I'm wondering if there's a direct correlation between file size and sound quality. When I search for a particular song, there are several different files I can choose from. Given that the file's are of equal length and they are all four-star quality (I've set this option), can I assume that a larger size file is of better quality than a smaller size one?

yep. for the most part that's right

Yes, every media file has a bit-rate. The higher the bit-rate, the higher the quality AND the file size (BUT it also depends on the length of the file).

If an mp3's length is 2 minutes, and it's size is 10MB it's excellent, but if an mp3's length is 60 minutes, and it's size is 20MB this mp3's quality is low.

yea, just compare like mp3's and download the one that is the biggest of the set. you should get a quality mp3!