1. I'll have to ask the upstream kernel maintainers if suspend/resume are supported and expected to work. I won't guarantee it.
2. In theory the kernel should handle the display device going away and coming back. Kodi only checks things at startup though so might not handle things properly even if things lower in the stack do. In either case the workaround will be (or should be) to run the 'getedid' script so the kernel (and thus Kodi) always sees the display device (via it's EDID data) as connected.
3. If you are using official nightlies please try the latest image in my testing share and see if that fixes the issue? - I've added some kernel options to make iptables work but can't remember if that change has made it into official nightlies. I'm also unsure if I added all the options for Docker though.