If you want to learn to type symbols and numbers faster with touch-typing, then you just need to learn to touch type. Mostly, it's practice. You could take a typing class, but could also probably find all the information you need, including a diagram mapping which fingers to use for which keys online somewhere. For example, the brackets are all typed using your pinky, which just has to keep reaching further to the right of the P on the keyboard. If you're typing a lot of numbers, I find it much easier to use a keyboard with a number pad on it than to type using the numbers above the letters. Then you use your index, middle and ring finger for the three columns of numbers, respectively, just as you would on a calculator/adding machine (yep, I'm old enough to have used those).
Everything else is just practice. The keys you use often, you'll have an easier time learning to find.