Can anyone tell me if the 90 days is in fact 90 nights? Can you leave the Schengen area on the 91st day? Or are you only allowed 89 nights and you are required to leave on the 90th day?
You get stamps that only mention the date and both the day you enter and the day you leave count toward the maximum stay. It's not 90 nights or 90 24-hour period or anything like that but 90 calendar days of (even partial) presence in the Schengen area.
More generally, following the rules is entirely your responsibility. Border guards can occasionally turn a blind eye but planning to leave on the very last day of your allowed stay and then finding your plane has been cancelled would not necessarily save you from a fine. By choosing not to have a couple of days buffer, you are taking a slight risk.