1990 Acura LS Integra A bit of a problem here please help?!

Ok heres the problem. my car starts up fine. then the car starts sputtering but doesnt cut off just yet. in park it is fine, then when i put it in reverse the rpm meter thingy goes below 1rpm and almost dies, sometimes it does die(the car) but it starts right back up when i start it. now once i pull off it takes off and is fineuntil i have to stop agian. I changed the spark plugs today and the battery also changed the air filter and i plan on changing the oil tommorow(i just bought the var off a family member, and i found out the spark plugs were never changed oil hasnt been changed in a yr and air filter never changed) also when i changed gears i notice the engine moves like when i through it in drive it shifts forward and reverse it goes backward a bit like it rocks somewhat then when i drive it drives at an angle like i need an alignment but i think its either a motoor mount or a transmission mount.. sorry this is so long just trying to give all info i have thanks for the help.