I don't mind answering the broach question. They are used to cut keyways in shaft holes, such as for pulleys. You have a round sleeve the same diameter as the hole with a square cutout the same width as the key. Put the sleeve into the pulley. Then the broach, a tapered, rectangular cross-sectioned, serrated cutter that fits into the slot, is pressed down (arbor press!) cutting the keyway.
I have never done it, but it would seem to me that a ground HSS tool held in a tool post on a lathe ought to be able to cut a short keyway as long as the setup is rigid enough, and sufficiently small cuts are made..
I have a small 1-ton Palmgren arbor press bolted to my workbench. It is useful for press-fit parts the size we use for models. Of course, the jaws of a milling vise can also act as a press. If I were to do it again I would get the 2-ton model. That said, neither of these would likely be capable of broaching in steel. The press at school is a big Dake model that is probably 15-20 ton.