Thrust Assymetry Compensation does indeed apply rudder to counteract yaw following an engine failure. From what I remember TAC applies about 95% of the rudder requirement, it's up to you to put in the rest.
As for the air conditioning system, it is typical Boeing. Air is bled from the engine compressors, pre-cooled and supplied to the air conditioning packs. These packs contain heat exchangers(utilising ram air in flight and air drawn through them by a fan on the ground) and an aircycle machine operating on a boot-stap cycle. In addition a trim air system is used to supply additional pre-cooled only air to the aircraft zones that require more heat. Also recirc fans are utilised. The entire operation is normally automated with master temperature control range set from the flight deck and individual zone temperature control (within master temp range limits) available from the flight attendants station.
Hope this is of help
Regards
Exeng