Yes
No, you have to have a base above zero to add it to.
No, you have to have a base above zero to add it to.
Don't forget that that if your base chance is 10% and your category bonus modifier is -15%, you are effectively at -5% which is read as 00%. To get your skill up to 1% you need to train/research 6% to reach +1% (-5+6=1%).
If you managed to augment this, with for example +20%, it would be -5+20= 15%, rather than fiddle with numbers, just say no.
As usual GMs are free to do want they want in their own games.