There are 2 problems I'm having.
1. The AC is weak. The fan speeds work properly and the air is cool coming out of the vents after a few minutes but it's not cooling the passengers enough! The girl I bought it from said her mechanic told her it's as good as it gets for an old compact car, but I don't know if I believe that-could need a freon recharge, right?

2. The car won't start sometimes (twice in a month). It cranks and cranks but won't start. After an hour or so I retried and it fired right up.

I would replace the Ignition Control Module, coil, and main relay. Here's how to replace the ICM and coil:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-hondas-46563-4.html#post265896

Yes, recharge the A/C. That should do the trick, as long as the condenser fan is actually coming on. If the fan didn't come on, then it would probably be the A/C & condenser fan relays ( or possibly the condenser fan itself).