Ahhh... My favorite Topic: Copyright Law
There was an older thread that discussed this that can explain and answer some of the questions here: Copyright music
now, to answer the questions:
1) Yes, if the music that the DJ is allowing for download is her own original work, although, she's not really that smart if she is, cause she could be making money...
2) No. That would be like saying Banana's from South America are illegal.
3) Napster now a days is a legitimate Music store. So is the iTunes music store. As for "free" music downloads. No those are not ok, no matter how you go about it (Unless you live in a country where there are no laws agaisnt it)
4) That depends. Are they for personal use, or do you sell them?
It all really winds down to the country that you live in. The US is really the only country in the world that actually cracks down, prosecutes and imprisions/fines illegal music downloaders.