This is kind of a stupid question, but I noticed that some loudspeakers have a couple black "drops" coming out from the voice coil. What are they and what do they do?
I'm assuming you mean "dark drop-shaped things stuck on the front of the cone" and not "drops of goo" ? I think this is where the voice coil wire goes through the cone so it can go to the connectors out back. If that's not what you mean, then please clarify.
Yep, those are the tensile wires that go from the voice-coils to the terminals. The drops of glue are to hold them in place and seal the cone.
All of the above. Usually there's a tiny metal bush inserted into and through the cone and the voice coil wires and the stranded tensile wires are soldered here. Some speaker have these "blobs" under their dust cap. So sometimes, you'll see them, and sometimes you don't.