91 Isuzu Stylus problems

Hello,
I am having two problems with my 1991 isuzu stylus (230K miles), and would need some insight
1. Lately, after rainstorms, my battery is drained, and after the car is started, the voltmeter pegs out, and all my electrical warning system switches like battery, fuel and brake light come on. On occasions the car starts to stall. I have been unhooking the positive terminal of the battery before rainfalls, and this seems to prevent both issues.

2. The radiator cooling fan hasn't been working lately, even though the repairman replaced the motor recently. I have ran the car in the idle position, and monitored the engine temperature and the fan for rotation, and after a few minutes, the temperature indicator approaches the overheat indicator with the fan still off. I have replaced the fuse, but still get the same problem.

I will appreciate any insight to the problem.
Thank you.