Napster was awesome. Think at the time you had CDs. You may have some mp3s from your own CDs and those of friends (maybe CDs you borrow from a library). Napster gave you what streaming is today (almost:
download times were not quick).
It was also a nail-biting experience... you'd have to wait 20, 40, 60 minutes or more for a song to finish downloading to find out whether the mp3 was the right one or a song that someone had renamed. Many times the song had been renamed maliciously from something by a different artist and you'd have to start all over again.
I'm pretty sure I played song fragments just fine as they downloaded, but I might be remembering that wrong.
Pretty sure that was a Kazaa feature, not Napster.
Download times varied a lot. Because it was peer-to-peer, it depended on how good your partner's connection was and how close they were to you. If you got lucky and found someone on the same network (or just a really fat uplink), you could milk it by browsing their shared files list and grabbing anything that looked good. It was a nice way to discover new music!
you also accidentally downloaded the wrong track just because it was mislabeled. many artists grew from that ex: soulja boy intentionally mislabeled his "crank dat" song as "50 cent in da club" etc