Pontiac Transmission/cooling system Question

I have a 2003 Pontiac Grand Am (V6), 92,000 miles with two years of payments left :( I'm upside down so there's no hope in trading it in, so I'm stuck with this car that is seriously starting to give me problems. Added to that, I'm a single mother with no mechanically inclined people in my life and I can't afford to take my car to the shop. So.I'm learning to work on my own car!

The "Low Coolant" light stays on continually, even though the coolant reservoir is full. However, I do notice that the liquid in there is all mucky and gross, more like stagnant pond water. The temp also sneaks past the mid-line on the gauge unless I'm moving faster than 45 mph (it starts to overheat when I'm stuck in traffic, etc. And I'm often forced to turn on the heater to make it cool down).

I'm guessing that something is preventing the water/anitfreeze from getting from the resevoir to the engine. How do I know what the cause is? It could be the radiator, the water pump, the hoses, or any other little pieces that make up the whole systerm, right? What is the most likely cause?

Also, my care is sluggish and the transmission seems to be having trouble switching gears (It's an automatic). It'll rev really high and whine so that it feels like I'm pressing the gas while in neutral. Then when it finally kicks into gear, the car will buck a little. The RPM's get up to around 4000. I read about the tranaxle sensor - could this be the problem, or do you guys think it's more serious than that?

Please help. Has anyone else had these problems? Are these things that a newbie like myself can fix?