There is a lot of good information in this board. To quickly answer your questions, I'll try and answer from what I know.
1. Do artists usually just apply the clay to a pbt keycap and begin sculpting away?
Usually? No. I'd be lying if I said that I hadn't tried this but, typically you want the finished product to be less than or equal to the height of a standard R1 or FN key, not larger than.
2. Does it stick to the key or do fire it then stick it to the keycap?
Not sure what you mean here. Everyone probably has a slightly different process in terms of baking or hardening a sculpt to prepare for mold production. If you were to bake clay on top of a GMK or PBT cap, you'd probably melt the plastic. Certain clays, like Monster Clay or CX5 won't harden from baking, the material will just melt.
3. Do they bake the keycap with the clay on the keycap?
No, see above. I believe clays like super sculpey are meant to be baked in order to harden, but thats just one material and makers seem to prefer different mediums. Everyone doesn't use just one thing.
4. How do they mount or position the keycap while sculpting? Do they put it on a switch/tester to hold it on place?
Binge, in collaboration with others, has been making the
Synth system. However,
Trovarion just posted
a time lapse sculpting session using nothing more than clay and a wine cork.
Other makers seem to have their own devices and methods for creating molds.
Just do some more research, experiment, iterate, try new things. Find out what works for you. It's a process.