1) If there's a suspend mode disable it and instead just remember to switch off your monitor when you get off.
2) Teej is right and it does sound like a battery problem... try running a program that ticks every second (or some kind of midi) and compare it to a bpm noise (one that's not a part of the computer) generator.
3) The CMOS is screwed.

It's actually quite easy to replace the battery, it's like replacing a battery on a watch. You just have to remember to ground yourself and read up on brain surgery.