~99% of the time it's clear who they're going to vote for, and their selection is a formality.
No doubt, and such will likely be the case this year, but the situation described above is without precedent, and electors might be faithless for a number of reasons, especially since there may be no state laws dealing with that particular situation.
I don't think it would come up. Surely the "exploratory" committee she formed several years ago would have advised her against running for president if she had been in poor health at the time. Pneumonia is bad--I was out of school for three painful weeks in the eleventh grade due to pneumonia--but she will get over it if that's really the only problem.