Idling problem - Low RPM's, Stalling

I own a 1996 mercury mystique, and when the car is idling and in drive, the RPM's will fluctuate from about 400-750, and the car will start to shake a lot when it gets lower, and at times the car will just outright stall. The stalling is more frequent when it is very cold, very hot, or it's in reverse and I'm not moving/backing up slowly.

In order to "fix" this problem (so I don't stall), for about the past year, every time I am coming to a stop or down a hill I will put the car from drive into neutral, which makes the RPM fluctuation less violent (from about 550-750), but if I (even while in neutral) leave the car to fluctuate on its own, it will usually stall out, so while I'm stopped and in neutral, I will rev the engine lightly in order to keep the RPM's at a constant ~1300, thus ensuring it does not stall out.

I would obviously like to straight up fix the problem, as I have no idea what it is.

I would also like to know if I am damaging my transmission while constantly switching from Drive to Neutral and back again, because I feel like it has to be wearing it out in some way or another.

Any help/advice I can get will be appreciated, thank you.