Yas-man

I'd visit anyway because it will give your more knowledge to make a more informed decision.
Also, they might already account for a certain percentage of people turning down offers when deciding how many people to accept (e.g. they accept 10 thinking only 5 will actually take the offer) that it's not necessarily likely that they would accept somebody else anyway.

A given candidate is not necessarily going to accept a position even if offered so it makes sense to invite more people than you actually need (especially if you really want to fill the position). Almost all programs will interview more students than they will actually accept because they know some won't be looking for when they interview them, some won't accept an offer, etc.
This doesn't mean I agree with being evasive about the circumstances.

Around when you have to leave the house (accounting for extra travel due to weather), look at the flight status. If there's no flight, just email (or call/text) the coordinator or whatever contact at the program and let them know what's going on. I'm sure they'll understand and work something out with you (Skype interviews, fly in a bit later, etc.)

Interview acceptance rates vary as the person above said. Different programs have different strategies because they'll have a specific quota in mind (e.g. they want to take 15 students) and they look at historical acceptance rates. They also have different budgets on how many people they can bring to visit (because of program funding or how many applications they get to pay for the other students) and use different strategies on how they evaluate people post-interview. For example, some programs will re-rank candidates post-interview via committee and some are merely making sure the student is a good fit.
You can generally estimate that the acceptance rate is 50% and then it varies beyond that point. For the last program I interviewed with, one could do the math on what they said their target enrolled student count was and historical attendance rates (how many students actually attend) and it was obvious their acceptance rate was greater than 75% to be able to meet that quota. However, a previous interview mentioned their acceptance rate post-interview was more like 40%.
They also will sometimes vary from year to year because a previous class size was bigger/smaller than they wanted, so they'll raise/lower the numbers the next year to make up for that. For example, if their previous class had an unusually high attendance rate, their funding may be overburdened so they'll lower the acceptance rate of the next class.

My student insurance is actually pretty good. But, it's really going to vary depending on the school. A given school likely has information about the plan, such as deductible and out-of-pocket maximum.