shared calendar sending change notifications when not turned on?

Yup. Add another one.

They are working on it.

http://www.apple.com/support/icloud/systemstatus/

Glad to see they are doing something about it, but hope that they are rebooting it or something at the moment because currently neither my reminders nor calendar are working.

Have the same issue but apparently it's been fixed. Haven't verified yet.

I'm still getting emails for every update.

I thought it was still broken too but it turns out that one of my four shared calendars DID have the "send email about updates" switch turned on in my husband's settings after Apple did their fix. I swear they were all off last night but today one was on. I suggest logging in to iCloud and checking that preference for each shared calendar you subscribe to. This has to be done on the receiver's end by clicking on the green "broadcast circle" next to each calendar name. Hope this helps.

I think any that you started and stopped are going to have that checked by default, and the only way to turn it off is on the iCloud website. I hope it's fixed but won't be able to test it until tomorrow.