Seeing if the motor mount is bad is pretty easy. Take a flashlight and get under the car (it's easier with a creeper, basically a rolling board with wheel that you can lay on) and take a look at where the engine meets the body. There will be one underneath each side of the engine. Underneath will be a "crossmember that connects the two sides of the car and holds the suspension in place, it's very hard to miss. The motor mounts bolt the engine to the crossmember. There are 2 possibilities: 1: one of the motor mounts, or both, (which are usually rubber in the middle to damped vibrations) are ripped and basically letting the engine flop around, or THE SCARY #2, the crossmember is ripped at where the motor mount mounts to the crossmember, which can also be an option, but more likely it's a busted motor mount or mounts. They're easy to find, but suck to have to replace. Oh, and tell your friend that no one in their right mind would take out or break motor mounts to show "how strong an engine is".
-For the speedometer, there's a cable going from the left side of the transmission (huge cable, hard to miss) and i believe that there is a bolt and a bracket that hold it in. The cable goes from the transmission to the inside of the dash behind the speedometer.
Good luck, these are really crappy problem to have if you don't really know how to fix a car!
By the way, it would be a better idea just to buy a GT if you want a V8 because it's cheaper and with the extra torque it stresses the frame, which from what it sounds like may not be in very good shape on your car. Hopefully the accident it was in didn't twist the frame much. If you want V8 power there are aftermarket companies that sell cold air intakes, superchargers and dual exhaust kits that would make your car as fast as a GT. Again, good luck, and congratulations on your first mustang purchase!
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previous name: 84stangLX
'84 Mustang 5.0 LX
my LX
'89 Mustang GT
my GT