How do I organize notifications on a Galaxy Note 10 - Seperate Messages from System Nots, Different Sounds, etc
You'll want to play around with the notification settings in your settings app. This is will be different for you, but on my Note 3 I go into the settings app -> Device -> Sounds and notifications -> application notifications. From here I can disable notifications for specific apps, and set apps as priority notifiers. imagine it's aomewhat similar with the note 10. Additionally, some apps will let you disable or change the notification sound from within the app, but here YMMV.

I'm not quite sure what you mean by separating system notifications and message notifications. 

As for making them appear on the lock screen, see if you can find a related setting under notifications or lock screen. This is also under "sounds and notifications" in the note 3 settings app, although this is again likely to be different for you.