Your Chevrolet Cavalier 97 might stall when going downhill because it has a bad fuel filter. It could also be the spark plugs misfiring.
Most likely a shot alternator, as far as misfiring it could be many things (bad spark plugs, clogged air filter, bad distributor, distributor cap) I would start with new spark plugs.
Bad plug or something is misassembled.
It is probably your spark plugs misfiring.
Bad plugs/coil/wiring
It is feeling silly and my other answer is it is behaving badly
Check spark plugs, plug wires, do a compression test
Check spark plugs and wires Do a compression test
The Ignition Coil is the one that cause misfire or Spark Plugs
check spark plugs and coil pack
8 spark plugs
check the coil pack