It sounds to me like two related problems. The speaker problem sounds like either a connector fault, a marginal connection or a broken circuit board trace. These are all similar problems from an electronic standpoint, and are basically equivalent to "the connection is broken because some physical thing isn't making contact any more." The stuck right click is probably either a case mis-alignment or something which broke off inside and got itself jammed underneath the button. If you remove the case around the keyboard, you can examine the area to the left of the keyboard and look for the connection problem. A good, strong flashlight and a magnifier might help. Once the bezel is off, you can probably see what's going on with the button. If not, probing with a thin piece of plastic can be a useful and (most likely) non-destructive way of finding out.
One other possible problem is foreign matter in the keyhole. If none of the other suggestions work, you might want to try blowing it out with compressed air. This is usually only problem for people with small children :-)
Possibly. I've had a fair bit of success handling problems like this by carefully removing the case and allowing it to dry for 2-3 days. Overheating is an overcurrent problem, so the chances are pretty good that this will work. Your chances can be noticeably improved by removing the battery and washing out the rest using deionized water (available at grocery/health food stores and major pharmacies). This will help remove any contamination from the water in the toilet. Case removal directions: iPod Classic Battery Replacement The reason I suggest deionized water: The existing contamination is water soluble. It may not be alcohol soluble. If you want to try alcohol, do it after a few good flushes with deionized water, since that will handle salt contamination. Alcohol is great for helping you get the last of the water out.