Most car ac systems are either on, or off. They don’t have variable compressor speeds. They cool at maximum until they reach the temp you set then they switch off. If the temp rises again then they switch back on.
A non EV cars heat is provided by the coolant that circulates through the motor. Nothing you can do will make the heater heat up faster.
Use “crazy glue” assuming this is a colloquial term for Cyanoacrylate, CA or super glue.
Fill the whole hole up, then drill it out with a drill bit a bit smaller than the diameter of the screw threads, then screw the screw in.
Just glueing the screw into the hole will not generate much clamping force and may not fix your problem.