Yes, it will work on a plastic.
you would be better off using a good quality sharp Forstner bit and backing the Plex with a piece of wood. these will work if you go slow and easy but you are taking a real risk of cracking the plex
The largest Step hole you can drill is 1 3/8
Probably you most likley will need to drill a pilot hole you most likley will need to oil the cut you wiil have to be careful to ensure continuous cutting to prevent work hardening of the SS
3/8" shank is the largest for this set
NO will not drill ceramic tile
China of course