electrical, multiple issues

I switched my engine a while back due to a timing belt failure after which my Aveo ran fine for about 10,000 more miles.
A few days ago the A/C stopped working, the starter on occasion will not crank and makes a strange click noise and the alternator red wire jacket melted off due to the wire overheating also a fairly new battery is starting to go bad.

I checked the ground wire connected to the transmission bell housing bolt and it is secure and clean, the rest of the wire loom is in good condition with no signs of fray/wear.

Help appreciated.

is the ac even an electrical problem?

what caused the wire to overheat?

how is the battery "starting to go bad"?