1) I think you covered all three types.
2) I've never heard of it. We've talked about the interesting absence of the sling in japan and China. This is a new name to me. Maybe you are on to something...
3) There are a number of names. We made a list a while back:
http://www.slinging.org/forum2/yabb/YaBB.cgi?board=1;action=display;num=10682423...4) Fustibalus is the latin name. It's called a staff sling in more modern times. I'm sure there are dozens of names considering it was used quite extensively around the world.
5) From what I've read, slingers could outfire and outrange bowmen in classical times.
6) Yurek, here on the forum, is approaching 1500 feet. it's not unreasonable to think a seasoned slinger could significantly out-range this. Compared to bows of the time, slings could out-range them handily. Xenophon noted that Greek slingers could out-range Persian bowmen by "no less than twice as far" (Korfmann), which were considered the premier archers of their time. (this was around 400 B.C.)
Chris