I am having some trouble fitting this into my dex210. Can these speed controls be run without the capacitor on them?

Not without a chance of damage. So No

Do not do it.....it will also void your warrenty if you have one....

If you have to, move the cap, but the esc will get damaged if you operate it without one.

I am thinking of getting a gtb2 with a ballistic 13.5 and was wondering if I can still advance the timing of the motor to give it a little more boost. I know the gtb 2 is for stock spec only but wondering if I can still mess with timing through just motor and that esc? thank you to anyone who has advice.

Yes, Ballistic motors have adjustable timing. Motor timing is completely independent of ESC settings.