I didn't see the second pic. That looks like it was peened on so the gear is probably on a flanged axle that would not come off unless you removed the axle from the bracket.

You might be able to get it off by using a hammer and a punch to try and narrow the side in the second pic so it will fit through the hole. Then have to peen it back on later. Or you could grind/file off the end sticking out in the second picture, but would likely have to replace that axle pin afterwards.

Can't tell for sure with all the dirt on it, but it could be a snap ring. It doesn't look like it uses the same e-clip as the other gear to the left is using.

Yes, you can swap the plugs on the wire.

However, if it is a 5W UK bulb, it will either not light up with US power, or will be dimmer, or might flicker.

You need to rotate the locking tab that holds the knob on first.

See that little tab that sticks out (visible in the 3rd, 4th and 5th photos in your link) you need to rotate that tab over and then the knob can be pulled off, once the knob is off, remove the collar that covers the screws to remove the knobs.

Its a 120v outlet on a 15 amp breaker and the washer was less than 15 amps. And 12 gauge wire is rated for up to 20 amps.

I have used a 12 gauge wire extension cord and just cut the female end off and wired it to a washer and it worked fine. The House had odd spacing between the water hook ups and electrical outlets, and none of the "washer power cords" were long enough, or I would have had to run long hoses for the water inlets and drain.

As long as the cord it rated for the current it should be fine.