Overheating?

Hi I have a 2002 pontiac grand prix its overheating while stopped but while going its fine the fans come on. I've replaced the thermostat and cap. Any suggestions?

Not sure if there working correctly. When car is turned off are the fans suppose to spin like a pin wheel when spun by hand or are they suppose to be locked into place?

They spin very freely when car is parked and cool

My car is overheating all the time. Goes straight up to HOT temp and shuts off automatically when driving it. Have tried replacint thermostat, waterpump, radiator, fans are working. Checked for any leaks and there are none. Even replaced senor. What can be the problem? Help.

Yes there on when it overheats the when sitting the temp gage gets all the way to the max and yes the upper and lower raditor hoses get really hot

Sometimes. I do have a radiator cap. Oil pressure is fine. When I took out the thermostat it seemed to run fine. It stopped overheating. Will It damage my car if I continue to drive without thermostat?

My Grand Prix is overheating. There is water in the system and in the overflow, but after driving it about 5 miles it went completely in the red and took a very long time to cool off. The fan is working. We think it is possibly the water pump. While driving it back home after it cooled (we let it set for about an hour) it immediately heated up to almost red again, but when making right turns the temp dropped drastically and then climbed again. Water pump? And if so, where is the water pump and how hard is it to replace. I am going to have to find a backyard mechanic to do this for me since I just lost my job and cannot afford a shop. Just need to know if this is the problem and what is involved in fixing it. Or what else could it be?
Thanks

Mine does almost the same except I go through lots of coolant and see no leaks and no water in the oil. What could that mean?

Yes, the engine is overheating. It was so hot the little bit of oil around the place you put in oil was burning off and creating a huge plume of smoke. And the heat coming off the engine was overwhelming when we opened the hood. The A/C went to hot air.I turned off the a/c immediately and had to coast the car off the freeway to a safe area, there was no exceleration. The small red light in the bottom right hand corner of the dash lights lit up (the one that says "temp"). We had driven only about 5 miles, but the air temp here is high. About 105 degrees. There is water in the system, even in the overflow and there is antifreeze in the water. The turning thing seemed really odd to us too. But after making the turn, the gauge went back up quickly.
We are very perplexed and because of my financial situation at the moment, I have to get this repaired as cheaply as possible. And return to my job search. Your help is greatly appreciated.