I am not familiar with that machine, but had the same issue with an older machine, a Singer 503A, where the clutch was slipping. I took it apart and wiped down the small clutch piece and the metal face on the hand wheel, which had oil on them, and the machine stopped slipping. I cannot tell from the pictures, but in the first picture it looks as though the clutch is still on the shaft; if that pulls off then I would try cleaning it.
I don't think the broken plastic piece is the problem; that appears to be a support rib for the inner circle on the hand wheel. If you want to try to glue it back then clean all the surfaces and try some plastic epoxy. Either way I wouldn't put too much torque on the hand wheel because without that rib there is more pressure on the remaining ones, making them prone to breakage; in fact I would examine the remaining ones for cracks and if you can get to them use the epoxy to fill any cracks.