I'm no expert but I play a little guitar. Just so you know...
1.) Yes and no. The rhythm guitar would probably be playing more or less along with the bass guitar most of the time as far as timing, but the rhythm guitar would be playing chords and the bass guitar would usually be playing a single note within that chord or another note that sounds good with it. That's good enough for general understanding, but they don't ALWAYS have that relationship.
2.) I'd say that the bass guitar follows the percussion more closely than any other instrument and serves to tie the percussion in with the rest of the band. I think without the bass guitar there would be perceptible gap between the guitar and the percussion. This is why a band can do without a rhythm guitar much more easily than a bassist. Once again this is not ALWAYS true (see The Doors or The White Stripes, etc.).
3.) Hard to say. I've often heard that rhythm guitar and lead guitar are sufficiently different as to allow for a guitarist to be considered as great at rhythm as another is at soloing if that makes any sense. For example, James Hetfield is widely considered to be the better guitarist of Metallica, and yet he limits himself to rhythm and singing while Hammett comes up with all the solos. Maybe they're just better at different things? Pete Townshend is considered to be one of the greatest "rhythm guitarists" of all time, yet that's not much of an accolade if rhythm guitar is by nature second fiddle to lead guitar. I don't know enough to be certain here.
