I get my motors from Sew-Classic. They are pretty much universal. She has or had two styles. The first style has adjustments on the side like yours. The other style is adjusted on the end. I've gotten several motors from them, I think the brand is Alphasew. My local SMG has the same brand and I've gotten them from him too.
You are right about the grease. The big gear in the middle right behind the stitch pattern nob.
I oil sliders, pivots, forks, but I grease metal gears.
Joe