Re: no sound or notification for calender
I had this issue twice on my iPhone. Once when I first set the tones in Settings it didn't give me a preview and when I got the first bunch of notifications there was no sound. I went back into Settings and checked the sounds and when I checked the first one it gave me a preview of the sound like it should and then everything was fine with the sounds. So try that go into your settings and under sounds check the sound you applied to the calendar reminders and see if you get a preview when you click it. If not try switching to a default ringtone and if the appointments make noise then resync your custom tone back to the phone and assign it again.
Yesterday again I got a bunch of iMessages and there was no sound. So I checked the volume and that the mute switch was fine. I flipped the mute switch to mute then back to regular and all my sounds were back to normal. It's the first couple versions of iOS 7 so there are going to be the little hiccups and glitches until it all gets worked out.