Others have pretty much explained everything, but I'll throw in a couple things...
Poacher said:
1. UFC/PRIDE/K-1; These are different entities right?
Those are the three main orgs, all seperate, and then there are a bunch of smaller orgs which these three kind of use as a minor leauge feeding system. A lot of UFC fighters start of in smaller orgs like, King of the Cage, Rumble on the Rock, TKO, World Extreme Cagefighting(WEC), Cage Rage, etc. Pride gets a lot of fighters from Shooto and Pancrase.
Poacher said:
3. Fighters can switch from one org to anoher can't they?
4. Do the champions of the respective orgs ever fight each other?
Fighters are under contracts, but contracts end and sometimes fighters go off to different orgs.
The orgs rarely send fighters to opposing orgs to represent them. The UFC sent over Liddell to fight in one of Pride's grand prix in hopes of setting up a Wanderlei Silva - Chcuck Liddell fight, but Liddell didn't make it past 'Rampage' Jackson, he did beat Overeem though. That probablly wont happen anymore, especially with champs, becuase the risk of having a champion lose to an opposing champion is too much.
Basically, Each org wants to portray their fighters as the best and if one sends their top guys over and they get whooped, it looks bad.
Liddell has lost in Pride, but Wanderlei has lost in the UFC as well. Once to Vitor Belfort and again to Tito Ortiz.
Poacher said:
6. Which do you prefer and why?
Thats hard to say.
LW - Pride (UFC doesn't have one anymore)
WW - Both Pride and UFC have great champs (Gomi and Hughes). The difference is, Pride's WW talent pool doesn't go much further than Gomi. UFC here.
MW - A little closer than WWs, but not much. UFC here as well.
LW - Pretty much a toss up, it so even. Pride has Silva,Arona,Lil Nog,Shogun, etc. UFC has Liddell,Couture,Babalu,Horn, etc.
HW - UFC's HW division is pathetic. After Arlovski, it is barren. Mir and Sylvia are alright, but neither is at the level of Arlovski or Pride's HWs. Fedor, Cro Cop, Big Nog, Sergei, Aleksander... Pride clearly wins here.
Overall, I like 'em both. UFC is also on free TV, so they get a bonus there though.