Brother your Accord idle RPM with M/T EL 1.6L engine is 750 RPM +- 50.
Most probably you have burned some wiring as this car has a very tough denso alternator rated at 65AH.
Check the 4 power cables coming from distributor to engine if they are leaking they will shine like stars at night.
DO NOT COME CLOSE TO THEM OR TRY TO TOUCH THEM AS THEY CAN KILL YOU.
The load resistance of wires should be less than 20K ohm for chinese one and < 8K Ohms for branded NGK / Denso & Bosh ones.
The car should never stop after removing the battery since the alternator take all load however it is not recommended to run the car with battery removed for long periods.
Have u checked the alternator belt tension and its pulley.
By hydraulic pump do you mean the power steering pump?
If yes then check that the power steering fluid is not dropping on the alternator.
CNG needs a very good electrical contact and more spark.