YES You can
First: you need to upload your Guitar Hero settings on the compuer.
Second: You can get the music from your computer and put it in the settings and save it
Third: You will find the song in bonus songs
how do I put the songs on my guitar hero 3 game? for PS2
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You could create your own songs, or you may be able to download songs and do the complex converting thing using a specialist program. Basically you can, but the process is long and complex if you have no idea what you are doing.
No. The PS2 does not have an internal storage device therefore it cannot download songs.
Go to the PlayStation Store (you need internet) there are individual songs and song packs some are free and some charge