A damaged catalytic converter could cause that.
Many problems could cause the car to stop accelerating. If the engine is running OK, then check a manual transmission for clutch problems, and an automatic transmission for possible slipping bands.
Fuel is not good!
Depending on the extent of the clog, it could cause the engine to lose power under a load or accelerating and in severe cases the engine may not run above an idle. I don't see it causing any one cylinder to missfire.
The most probable cause is poor fuel or water in your fuel. This could also be due to the timing being out of proper adjustment.
Could be as simple as a tune up.
Perhaps it is your pcv valve or rubber elbow connector that is hooked up to the pcv valve.
Slow engine RPM is the main reason a car may be sluggish while accelerating. However, it also could be due to the oil.
could be a bad plug
could be two things. if it does it while idling or accelerating, then its probably a spark plug not firing. if it only does it while accelerating or under load. then its probably a spark plug wire. either way, as general maintenance its a good idea to replace all the wires and plugs. Clogged catalitic converter will cause it to lose power.
Yes and No, they could cause them to get into more trouble.
Check for a busted engine or tranny mount.