[Multiplayer against AI]

A skirmish mode. I think it'd be fantastic. A good way to test out different strategies. Nice, contained, single missions.

[Should I uninstall Civil War Overhaul to continue a previous save?]

I get the feeling you didn't read the mod's page. There's a section there where Apollodown talks about "Skyrim Sorcery". It's not a law, as there are exceptions, but it applies to large mods that modify a lot of scripts, like all of his mods (except perhaps Info Overhaul), Sands of Time, SkyRe, etc:

 

Never install mid-game, and never uninstall mid-game.

I did read that actually. Now that you mention it. Consider that question answered then

[Should I uninstall Civil War Overhaul to continue a previous save?]

Nope... a mod like that should never be added in half way threw a save. Only when using current ones created with it. Or new ones

Ok, so I should uninstall to play my previous saves?

[Should I uninstall Civil War Overhaul to continue a previous save?]

So I've done some googling and reading on the actual nexus page of Civil war overhaul.

I need to start a new game to use the mod <<<< I get that.

 

BUT, as for my save that I'm already playing with, can I still use that and just not touch the civil war questline? Or should I uninstall Civil War overhaul if I want to carry on with that save?