1. This is not really a single question with a single answer
I think vaguely what you are asking is if you can root without tripping knox?
Nope. Not at this time.
2. If you use CF-Auto-Root you'll likely find that the vast majority of applications keep working without issue. Of those that don't, a handful you can manage back to a working state with various tweaks, but there are a few that are probably gone for good. You can basically kiss all the Samsung hub apps goodbye, these will start claiming they are not supported in your country even if they were working perfectly prior to rooting, some may continue working for a short time after but eventually something leaks and your access is cut. Screen mirroring will no longer work though this can be fixed with a small zip file flash. OTA updates are also gone.
Forget all the talk about 'triangle away' fixing any of this, it hasn't for me.
3. Odin is a tool that is able to flash firmware files or parts thereof to your device. Heimdall is an alternative suite of applications, while there is a GUI for it, it seems fairly hit and miss on Linux these days, I've never had much luck with it, on the other hand the command line tools work perfectly fine.
Once you trip Knox, there's no turning back! You won't lose your warranty in any meaningful way, but you may end up having to argue about it and drag in government regulators to get your tablet repaired free of charge depending on the dealer response.
4. I don't think this is particularly relevant to the SM-P600. My subjective opinion would be to stick with the bog standard Samsung ROM. If you want cool themes there are a multitude of launchers, Xposed takes care most other things you might ever care to tweak.
5. You have one choice. CF-Auto-Root. Backups are healthy.
6. True, but you'll still be able to flash via Odin so it doesn't really mean much of anything. Once you trip Knox, you can also kiss OTA updates goodbye as well.