1. Technically, as long as the song is in tangible form, it already is copyrighted (Berne Convention). However, as you said, for it to stand up in court, the best way is to register it through the U.S. Copyright Office. This can be done online for about $35:
http://www.copyright.gov/forms/ If you're in Europe, I believe there's probably something similar through the EU, though I'm not sure.
2. Yes, it should be copyrightable. When you copyright a song, it is only the melody and lyrics which are copyrighted. So, theoretically, there's no minimum number of notes required for a copyright. You just need to show originality. So, provided your fragments show that, it should be O.K.
Hope that helps.