Mine crashes frequently as well, but sometimes it magically works. When that happens I find as long as I never "back out" it remains open and will continue to work. I've noticed no pattern that would explain why it crashes some times and not others.
The live tile used to work for me, but since I got a replacement band it's been busted. It also does not actually seem to sync in the background so I need to open the app to get the band2 data to sync to Microsoft Health.
And yes, it's allowed to run in the background (if it's not it will...
Has anyone with the new firmware noticed any improvement with the camera? Specifically does it take less time to "apply finishing touches", and does it no longer make the image worse when it's done?