1992 Nissan Maxima Sputters when driving and loses gas powe

Engine Performance problem
1992 Nissan Maxima 6 cyl Front Wheel Drive Automatic

Car sometimes loses power while driving all of a sudden and shuts off. I can restart it but it is difficult and I may have to press the gas for it to turn over and sometimes when I do the rpms still drop all the way down to zero. Sometimes while driving the rpms will drop and if I keep my foot steadily on the gas it will sputter, lose power then accelerate then lose power then accelerate. Sometimes it will catch and smooth out then drive fine. Sometimes the rpms still drop to zero and the car cuts off. The problem seems to happen if I step on the gas suddenly or with a lot of pressure. If I take off smoothly and easy the car seems to function better. Sometimes when about to stop I may put the car in neutral and this seems to stabilize the rpms a little. I noticed the problem right after filling up at the gas station. I thought it was bad gas, put dry gas in it but the problem still persist. A problem that may or may not be related - Prior to this current problem Some mornings starting the car is difficult but once the car is warmed up it starts fine. Other issues. A motor mount is broken and there is corrosion on the battery. I understand this issue can be hard to diagnose but hopefully my explanation can help you to help point me in the right direction. Thanks.