89 honda accord issues

So I have an 89 honda accord dx automatic 4 cylinder. It only has 66000 miles on it and was decently taken care of before I got it. The first problem that I am having is when I come to a stop the rpms drop below 500 and the whole car shakes. The second problem I am having that just started about 2 weeks ago is that when I go to accelerate from a stop the car has what I call a fart. What I mean is that I will accelerate and the rpms will go from like 2000 and then drop a 1000 then go back up and then go down. This happens even when I am at a cruising speed below 45mph. ONce I am on the freeway there aren't any issues. The best thing I can think of is its like the gas is spraying in and then it stops for a moment and then starts again. I have taken the air filter system of and checked all the lines that I can see and i did find one that needed to be replaced and I checked all the gaskets and they look good. ANy ideas would be greatly appreciated.

it could be dirty fuel injectors, try using fuel injector cleaner (use double of recommended) in the fuel tank (can take a few days to work in).

if it starts to get better, than you need new or rebuilt injectors.

if after a few days or week, and it doesnt get better than a sensor is going bad or dirty.

the shaking sounds like your engine mounts are either worn out or improperly installed

The 89 DX has an A20A1 or A20A2 (A2 most likely only if originally purchased in California), both are Carbureted - 2bbl Keihin ( Feedback Carb )
I would check for a vaccuum leak, as the vacuum advance timing could be causing both problems... of course taking apart and cleaning your carb aint a bad idea either (can't hurt unless you lose a piece ), a gunked up carb could also cause both problems, the car is 20yrs old and having only 66k on it, it must have spent a fair amount of time sitting around... carbs don't really like that too much.

Good luck!