The first thing to make clear is that there's no such thing as a P2P 'site'. The very nature of the peer-to-peer system is that your PC is effectively connected directly to someone else's PC, so that files can be transferred in either direction.
Morpheus, Limewire, BearShare and many other programs all do the same job. i.e. they allow you to connect with the Gnutella P2P network. (Some programs also allow you to connect to other P2P networks, such as the Neo network). This means that the results you'll get from any particular program will be fairly similar to any other program.
However, if you're finding that one of these programs doesn't meet your needs, it's easy to try another one. Limewire is the most popular but BearShare seems to be gaining in popularity:
http://www.limewire.com/
http://www.bearshare.com/
I've no idea why Morpheus should be giving you messages about 'unauthorised downloads'; this is true of almost
every file downloaded with any P2P software!
Downloading copyrighted music is a civil offence (for which you can be sued) but the nature of the P2P system means that music files on your PC become available for
uploading to other people's PCs. The law regards this as
'distribution' which is a criminal offence (for which you can be fined or imprisoned).
Chris