I don't think welding the rear axle is technically legal but it should work fine if you are careful when you grind it. Don't dig into the axle and leave nicks which can create stress concentrations. I agree that getting hit will load the bearing and it was probably getting close to going anyways.

Fix it and run it again.

No, I don't weld the collars on my Capri axles but not sure if there are issues with Pinto collars coming loose under racing conditions.