This is the forum area for MegaMek, the computer implementation of BattleTech - you seem to be asking questions about BattleTech in general, which are probably better suited to another channel. However, the answers are also in the BattleTech rules (either 'Total Warfare' or 'BattleMech Manual', depending on which you are using.
In brief ...
a) Heat builds up each turn, based on your movement speed and the weapons you fire. The effects of overheating are detailed in the rules.
b) You roll for location when hit, and if the armour is gone, or if a through-armour critical is acheived, you roll on the relevant critical hit table. Again, this is detailed in the rules.
Heh. Ninja'd.