Is Teeth Whitening Safe if I'm Prone to Cavities?

Many whitening gels have fluoride in them, so that could help. However, the decayed area may become sensitive due to the dehydration that occurs. This discomfort is temporary but should not be ignored.
Whitening should not weaken teeth or make them more prone to decay. As long as the gel was dispensed from a dentist you should be fine.

I will sometimes do whitening first then match all the new white fillings to the surrounding tooth structure. It looks great! As a dental cavity prevention treatment, it's not intended for that, but what I've found is that people with whiter teeth will brush and floss more often so it can improve your hygiene over time.

It depends where the cavities are in your mouth. If they are biting surface cavities, I usually recommend that my patients have them filled before whitening. I prefer that the tooth structure be as healthy as possible before starting a whitening regimen. Also, the bleaching trays that we use fit so intimately that changing the tooth structure after the initial whitnening impressions are taken can alter the fit of the trays.

If you are reasonable with how often you whiten, it won't change the enamel structure.  You're teeth will therefore be as resistent or prone to decay as they always were. If you have any existing decay get that taken care of first and then try whitening them.

It's best practice to restore decayed teeth before you whiten your teeth. If you have very small cavities (decalcified areas) that you are treating with fluoride or another recalcifying agent, it should be safe to whiten at the same time. Whitening will not make you any more or less prone to tooth-decay.