I am quite new to this game and I am not sure if this is supposed to happen or not, but every time I click start a new campaign, it resets my rank and all of my BP and XP. When I exit out to the menu it still shows all of my previous stats. Is this a bug or do I need to search some more through the game to find the problem?

Might be a bit on the late side, but I think this is not a problem.

What you are seeing in the main menu are your overall kills, death 'n stuff, Rank and RP are not saved between new campaigns,

As for multiplayer, your rank, Rp, inventory and stash is saved between all official invasion servers.