I haven't loaded up the mod manager in months, but I went to start a new game earlier this week and I could not log into the mod manager. I still can't. What is going on there?

Also, if I start a new character and somehow log in later on, will deleting certain mods such as the one that adds battles between imperials and stormcloaks everywhere, and the one that adds a ton of NPcs in the world mess with my game potentially?

Mod Manager has been undergoing changes. If your version is old enough, it won't even work. You'll have to download a newer version manually to fix it. Or it's related to the general overload the Nexus is having as a side effect of the Steam Summer Sale.

Yeah, if you're planning on removing some mods, best to do it before you start playing. Uninstalling mods always leaves some data in the save & those scripted encounters & spawns will keep being called, potentially slowing everything down later on.