SewExtreme, I do not know what the broken part is. However, if your Bernina oil is actual sewing machine oil, it will be fine with your new Featherweight. That particular Featherweight is the slowest and least able of the Featherweights and it is not surprising it sews slow. However, check the belt. It should be loose yet able to turn the machine. You WANT it to be loose. It was designed to be loose and won't prematurely age the motor that way.
Cricket