weren't they all dead? all but one who for reasons I don't know changes appearance every now and then?

The time lord were locked in "The Last Great Time War" agents a race known as the Daleks who would go on to destroy everything non Dalek. Driven to madness and desperation they implemented a plan that would tear the fabric of the universe apart while they transcended into beings of pure consciousnesses. The Doctor could not let this happen and modified a time lord weapon know as the De-Mat gun that could remove something from the space time continuum into "The Moment" A weapon that could remove all of whatever was shot. He used it to destroy the time lord's home planet Gallifrey along with the time lords and the Daleks leaving very few survivors on ether side. As for the shape changing upon death a time lord enters a state of rapid regeneration in witch every cell in the body is replaced leaving them with a new body, new personality, but leaving the memory. However each time lord has only evolved 12 regerations and upon the 13th death the time lord has died.

Wouldn't Matt Smith be the 12th then? Because Tennant did that half regeneration thing where he put the remaining regeneration into his hand. If so, does that mean after Matt Smith no more Doctor Who?

Technically 10.5 does not exist anymore is series 5 episode 3 "Victory of the Daleks" It's said that the planets in the sky event never occurred thanks to the cracks in time rewriting history, If this is the case 10 never ran out to greet Rose and he was never shot by the Dalek and in fact none of that ever happened so if that's the case Rose never stops searching for the doctor because the meta crisis doctor never exists and stays with her and the Doctor Donna never occurred because she never touched the hand with regeneration energy as well so she never had to forget him. And that also means when 10 fought the master again he still had his hand and after he absorbs the radiation he could just put the energy in his hand then, so basically he never regenerated so even 11 should no longer exist. I should probably stop before I rip a hole in the universe.

My brain is full of fuck.

There is a debate about 10.5 but the argument is that the had had enough regenerative energy to create a human doctor

I know I'm kinda late on this but I think when he defeated The Master the last time he somehow restarted his regeneration cycle so Tennant was kind of like generation 0 and Matt Smith was like the 1st in the restarted chain. Not totally sure though.

Well wasn't the "12 regenerations" thing a Time Lord law? The Doctor being the only one left now, (other than like, that one clone and maybe Susan I guess) the laws of time itself are kinda just his to fuck-about with are they not? Who's to say The Doctor couldn't just Regenerate indefinantly? (is that how that would be spelled?)

He usually does, yeah, but having recently seen all the Tennant specials it's hard to be sure (I loved the one where he beats time itself, it was like The Doctor kinda fell, and learned the first important life lesson in a hard way in many many years, if that makes sense).