1) You've got them all. They are all listed on p. 58 of the BMM for convenience. Note that the heat damage only applies if you life support has taken a critical first.
2) Not at the intro level you specify. Tactical Operations, Strategic Operations, and A Time of War deal with those things.
EDIT: Specifically, tournament-level rules are not concerned with the fate of a mech (or its pilot) once it is destroyed. For Total Warfare-level purposes, you can assume the Mechwarrior can survive any damage that does not destroy the head, score a critical hit on the cockpit, flood the head with water, destroy the entire mech in an ammunition explosion, or inflict the 6th point of damage directly to the warrior. Rules for ejection and other forms of abandoning units are advanced, and can be found in Tactical Operations, page 196. Rules for healing injuries can be found in Strategic Operations, page 187. The Chaos Campaign rules beginning on page 156 of Campaign Operations also has rules for healing pilot injuries.
Thanks to Weirdo for the extra info.