Hard to say on the speed. Could be the phone, could be a network issue. If your settings (e.g. APN settings) are correct I'd speak to your carrier.
As for music, what format, what music apps, and where are you putting it? I'd check the music player's settings to make sure it is scanning the folder the music is stored in, or tell it to rescan the device. Also make sure there isn't a ".nomedia" file in the folder you've copied the music to.
And if in doubt, try a different music app (e.g. PowerAmp) to make sure it isn't a problem of the built-in app.