The one in yor hand looks like something you would use to mill flat a surface with a pilot hole, like a stub boss. all cool stuff, jest keep screwing them together and see what fits! The tapered piece looks like a swager of sorts?
The one in his hand is a spot face tool.... Probably for a drill press or a Bridgeport... Damn, that's old!!!!.....
The one in your hand is for repairing the seat in your household taps, Remove your tap/faucet or whatever you call it, lightly screw in the large tapered area then turn the handle clockwise to face the seat. ^^^^Marcos beat me to it.