Basically, I want to get some mods for single player, but not multiplayer. I don't play on a mod server, so either it wouldn't be fair or I would be kicked off (I don't know how it works). So, is it possible for me to install mods on single player but not multi? Would I have to remove/re-install all of the mods when I switch back and forth between single-and multiplayer?
Yes you can run mods for single player and then play on a vanilla server. However, the mods that require a server-side counter part wont work. You will still be able to see the creative mode tabs and such, even give yourself items from them (assuming your in creative mode, of course.) but the moment you try to use them or place them into the world, they vanish.
But client side only mods, like some of the mini map mods, they still work just fine. Barring any server side operations, though.