If I understand you correctly the car will accelerate from a dead stop and go through 2nd gear, then into 3rd gear where it drives fine, then when you are slowing down it will drop back into 2nd but will not drop back into 1st and then the car is very hard to stop.
This sounds like your throttle body butterfly valve is not completely closing or there is something wrong with your throttle position sensor, for some reason the car still thinks you have your foot on the gas pedal and until the right conditions are met (engine RPM and car speed mainly) the transmission will not drop back into 1st gear, this is where I would start.
The rhythmic thumping from the back end of the car sounds like an out of round brake drum, this is usually caused by the brakes overheating while trying to stop on a long steep hill and then immediately putting on the parking brake and leaving the car sitting for several hours, the brake drum ends up cooling off in an oval shape. If you have disc brakes in the rear one or both of the discs is probably warped.
What do you mean by: "If I try to put it in reverse it will kill."? Do you mean that when you put it into Reverse the engine instantly stalls and dies?
Yes the Owner's Manual says that the transmission fluid does not need to be replaced for 100,000 miles but my 1999 Esteem's automatic transmission's fluid was brown and burnt at 77k miles and had to be replaced. If it is burnt, Valvoline makes a transmission fluid for cars with over 75k miles, I would start using it now, I am at 133,000+ miles and have no noticeable problems with shifting.
Hope this helps.
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