Buckwheat will regrow after mowing if cut before it reaches 25 percent bloom. Stubble should be 4-6 in. It also can be lightly tilled after the midpoint of its long flowering period to reseed a second crop. Some growers bring new land into production by raising three successive buckwheat crops this way. Earlier, the stubble tends to regrow, later the first seeds mature and germinate. Earliest maturing seed can shatter before plants finish blooming.

Yes you can overseed radish into buckwheat, generally before Sept 1. Getting good seed soil contact will be very important for stand establishment. Here are some good resources: https://www.nrcs.usda.gov/wps/portal/nrcs/detail/mn/technical/?cid=nrcs142p2_023671