i was wondering if I could use the $50 microcontroller for a sumo robot
Sure, you just need to make another program for it of course.
and can I add some crystals to it? What other things can I add to improve its performance?
You can add a crystal, but you won't get any improved performance for what you wanna do, from doing so.
Not sure if you mean improving a Sumo or improving the controller?
I know it would be better to just buy another microcontroller but actually what i most like about robotics is building the microcontroller myself.
Let's be clear on the concepts. The microcontroller is the actual chip (which you aren't able to build). When you stuff it into a board, you get a microcontroller board
If building the board is what gives you a buzz, you don't need to confine yourself to robotics - almost any piece of electronics can be made with a microcontroller (although it sometimes makes no, or very little sense).
For a Sumo the "$50 board" is more than enough and you'd gain absolutely nothing by using a more capable board.