Missing calendar events and can't create new ones
Go to Settings and click iCloud and turn on Calendars.

If that doesn't work, while in your Calendar, look at the bottom - "Today," "Calendar," and "Inbox." Click on Calendars. Somehow my "Home" calendar (which is where I save most entries, as opposed to "Calendar" or "Work") was unchecked. I couldn't see any old or future entries, and when I added entries and hit save, the day would be empty. When I re-checked "Home," everything reappeared.

It just wasn't showing "Home" entries. I hope your problem is this simple because I know how you feel like you're losing your mind when something like that happens!