Looks like the pump bearings are locked up, a new pump will be needed. If you remove the rubber coupling the motor will probably run. A GE washer won't gravity drain due to the high loop in the drain hose.
The UV bulb or Ozone bulb is actually an arc lamp. The filament is to preheat the mercury vapor until the arc starts. Arc lamps need a ballast to limit the current flow, some used a 40 watt light bulb others had a small magnetic ballast.
I remember working on one of those years ago, it took me a minute or two to figure how to stop it, you have to open the door! You would think they would have put a cancel button on it.
When you tapped the coupler onto the motor shaft did you support the other end of the motor shaft? I have seen motors bearings damaged by not supporting the other end. Try removing the pump and the motor from the transmission, run the motor by itself and see if the noise is still there.
Oil smell
A GE Filter-flo washer transmission is sealed and does not have a vent hole like a Whirlpool transmission, unless you have an oil leak, I don't see how you can smell the oil. My guess in what your smelling is coming from the warm motor bearings, this could explain why both washers...
The damage around the roller shaft is caused by the steel wave washer behind the roller. I have seen them cut all the way thru the metal, and the shaft and roller drop off! All replacement rollers come with plastic washers to replace the steel one. Be sure not to reuse the steel washer.
Check the filter
The first thing to check is the filter in the bottom of the tub. If it’s dirty or clogged it will prevent water flow to the pump. This will cause the dispensers to not open.