The "battery" light may go away with use but its probably the alternator not giving out enough charge.
Overheating - check the fuses, there is one in the fuse/relay box on the front slam panel. Its a funny fuse, just a piece of metal cut to shape. There are others but I'd have to check the handbook.
Aircon fan, there is a cut out for the compressor when there's no gas and also fuses for it.
Do you have a handbook, they are all listed in there.