I think in principle a presidential candidate's health is fair game. The Vice President taking over in the event of disability or death is a safety measure built into the system, not an ideal outcome. Someone who knows they will not live to the end of their term(s) shouldn't run. Roosevelt '44 was irresponsible and an abuse of the American people. If either candidate is failing to disclose a serious medical condition, i think they should face punishment for doing so.
On the subject of the candidates: Trump is a 70 year old man who by his own admission does not take care of himself at all. He doesn't eat well, doesn't exercise, and rarely sees a physician. His doctor's note is crazy. On the other hand he seems to have aged fairly well, he quite possibly has good genetics, and he's not likely to die by the end of two terms due to age-related health decline. I think it is reasonable to apply scrutiny to his lack of disclosure and indifference to his health, but there's probably not much else there. Hillary is a 68 year old woman who seems to exercise regularly, eat well, and take care of herself by working with doctors. However, a concussion and blood clot is a somewhat serious recent health issue and I think it's reasonable to consider that, like it was reasonable to consider Biden's brain aneurysm. Again, however, she is pretty unlikely to be dead by the end of two terms due to age-related health decline. I do think that the relatively advanced age of both candidates is notable.
The recent Hlllary health stuff is total crackpot fantasy reddit nonsense. It is not unusual for candidates to get colds, or flus, or jetlag or other travel-related illness, or to faint, as a result of a grueling campaign schedule. George Bush vomiting in Japan is not a relevant thing. The conspiracy is self-reinforcing, because routine health things that happen now "confirm" the conspiracy. I am very thankful that the majority of people reading political subreddits on either side of the political spectrum are either not old enough or too lazy or stupid to actually vote. I have no idea why anyone would voluntarily admit to reading some of the shit out there; you are acknowledging that you are a credulous rube. The handful of die-hard Trumpers we have here make it clear that they get their news by reading Trump reddit and 4chan 18 hours a day. There are no shortage of Hillary idiots here either, but most of them seem to actually get news from news sources and not @WhiteGenocide.
If Ruth Bader Ginsberg or Betty White ran for president, I think it would be right to point out "Look, these people are too old and not healthy enough and they will be dead by the end of their terms". I don't think that's ageism or sexism. I don't think "the VP would just take over" is an invincible defence.
With respect to McCain, he was also an old guy, also had a history of health problems, and had a physical frailty that seemed caused by his torture and captivity in Vietnam. I think criticisms or observations about his health were reasonable at the time, although some hysteria around it might not have been. I don't think any VP pick would change this. I do think the fact that he picked a VP who a) was clearly not ready to be president in terms of experience, and b) was an absolute nutcase makes his health more relevant.
Both current candidates have picked reasonable VPs. Kaine and Pence both have lots of experience and are well-liked within their parties. It is difficult to argue that either of these people are, on their face, not qualified to take over. Kaine is seen as boring and moderate, while Pence is seen as boring and highly conservative. If you're supporting Hillary from the left then you might have some reason to worry that a Kaine presidency would be more moderate than you like; if you're supporting a Trump presidency then please don't vote but also you might be worried that Pence gets distracted in traditional social conservative mud instead of building a wall or nuking the families of people who joined ISIS or whatever it is you want a president to do. But despite these minor fears, we can take comfort that there's unlikely to be a radical disruption of government if one of the current VPs takes over.
Finally, on the subject of "Why Hasn't She Made A Statement Yet". This kind of breathless idiocy makes no sense to me. It was OK for George W. Bush to take a few minutes to process 9/11. Michael Moore's ranting about how No One Knew Who Was In Charge was baffling then. Campaigns and administrations are big organizations, and while it's important to have clear authority during situations, it's not important to have a press statement within 15 seconds just because idiots F5 the internet incessantly.
If this is a serious health issue, then it's more important to ascertain the consequences than issue a provisional statement. You'll live in there's a few hours where you don't know what happened. If it's not a serious health issue, then again who gives a shit? I agree that from an optics perspective poor communication might help confirm conspiracy theories, but conspiracy theories are also self-confirming so it's not clear to me that the response would be any different if she had issued a statement 5 minutes later saying she had indigestion.