For the heater blower, I'd turn on the fan, break out the voltmeter, and see if you're getting steady electricity to the blower (check the voltage at various fan strength settings). If not, you can work your way upstream. If you are and it's still not working reliably, you just need a new blower. You can probably find a used one for a good price on eBay or a pick-a-part. If you need help working your way upstream the electrical circuit, post back and I'll see if I can find some resources for you.
For the climate controls, pull off the dash bezel around it. Once you've done that you should be able to remove the controls, unplug them, and find the bulbs in the back.
Check out this thread for info on bulb sizing, where to source them, and LED alternatives. Half of the interior lights on mine were out when I picked it up too, but with a bit of effort I've converted them all to white LEDs
As for the CD player, I'd consider it a goner. It's not uncommon at all for CD players of this age to head south, and the first thing is always the slot loader. If you're set on sticking with a factory unit, the best you can do is grab a used one on eBay, though for the price and effort you could probably get an aftermarket unit that has bluetooth, aux in, and can talk to your phone
