ToME: the Tales of Maj'Eyal

How many additional category points do characters get, and when?

You get points at levels 10, 20, and 36.
There is also another point available through a boss drop late game, and Cormacs start with 1.

Or you can play with the no locked categories addon... And use them all for mastery improvement and rune slots.

Aren't there further bonus cat points in the infinite dungeon, something like every 30 levels after 50 or so? Or am I misremembering the information I read?

You get an extra category point at l46 to make up for not getting the sandworm heart.

Infinite dungeon addon also gives you one at lvl 66 and every 30 after that.