Mod manager:
http://www.racedepartment.com/downloads/actools-cars-manager.6518/
I've not used it.
Mods work online if whoever has created the server has included a particular mod in their server config. Short answer: Yes.
If you see cars/tracks that are written in red, it means that you don't have that content.
Don't know what's going on with your online thing.
Before you join the server, it should show you the relevant information regarding whether the session is in practice, qualifying or race.
Are you sure you're not joining a race that's already in progress, or a practice session?
There are plenty of good mods mate. Have a look through the links posted by myself and Borsch further up the page.
The ones on Race Department do have a lot of feedback to give you a good idea of what's decent or not if that helps.
Other than that, just try whatever piques your interest and delete it if you don't like it
On another note, has anyone tried the URD PX1+2 LMP cars yet?
They're excellent!
Yes, they are paid mods, but these guys make very high quality stuff - including making cars on behalf of Kunos for official DLC.