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.
could be a broken engine mount.
Could be a misfire. In need of a tune up.
the clutch release could have broken , the brakes could have locked, the engine could have blown, the transmission could have broken. These are mostly things that have happened to our ranger. It depends what you mean by stops
Yes.
The engine is running rough. Could be in need of a tune up.
If it's a severe vibration, expect a bad mount. If it's very slight, that might just be normal operation of the reciprocating engine.
A clicking noise in the engine of a 91 Ranger could indicate a problem with the valves. A valve lifter in the engine may be worn or stuck.
Turning on the radio will not cause your car to vibrate. The only thing I can think of that would even be remotely possible is that the alternator is barely working enough to keep the battery charged. The extra load of the radio could possible cause the engine to miss. This is highly unlikely, but remotely possible. Have the charging system checked.
motor mount could be bad or broken
The most probable cause would be the idle control on the engine. When you put a car in gear, there is a "load" put on it (the transmission is using power) and the idle speed normally drops. The idle could be dropping to the point where it becomes unstable and causes the engine to vibrate.
If you have a 2 piece driveshaft it could be the center carrier bearing.