It does, but here's a tip if you don't want to waste limpets. Peck an asteroid with your mining laser BEFORE firing your prospector. If it drops one fragment of what you are looking for (say, LTDs), then hit it with a prospector. That way you get maximum yields of what you want without wasting limpets on dud asteroids.
I would suggest against this. Lasering off fragments before prospecting will cost you fragments and therefore make you mine slower. Generally, having several active prospectors will make you prospect significantly faster than you could if you need to reach a rock with the lasers first.
Depends on the size of the ship and if the number of limpets one can carry
Probably from a time when Cmdrs were actually limited in CRs to be able to afford a large mining ship