As you know there are a lot of games that make you wait a lot of time, for loading, crafting, lobby waiting, queuing etc. so I was thinking about getting another monitor but I'm not sure how this would work.

How do you switch your mouse and keyboard from one monitor to another?

If I watch a video on one monitor and have a demanding 3D game on another like Battlefield 3, would the performance be drastically reduced?

Do Nvidia cards even support 2 monitors at the same time?

If been running a dual monitor setup for a while, playing a video on one and a game in another with a HD4890 and before that nVidia 7900. I've seen no performance hit for 3D.
If you want to work on screen two you have to alt-tab out of the game. I always queued videos so I don't have to switch too often and I ran IM on screen two. Reply unfortunately only by alt-tab.
Maybe you're adept in LUA (if the game supports it) so you can program IM in game or controls to other programs.

When you plug the second monitor in, it'll probably default to mirror the first monitor. Right click on the desktop to get into monitor preferences and change it to extended desktop. You can set up what ever you like on the secondary by dragging the window over. The game will run on the primary monitor. Games can usually run in 3 modes: Windowed (can be sized), windowed (fullscreen), and fullscreen.

Windowed modes mean the game uses the preferences for the desktop for gamma, etc and you can just move the mouse in/out of the game making something else the active window.

Fullscreen mode - utilizes all of the graphics settings set in the game and you use alt-tab to switch in/out of the game to another window. This generally gives the best gameplay.

Power use: Unless you have an Nvidia GTX 6xx card, there's a significant idle power adder when you run two monitors. AMD and earlier Nvidia cards do not downclock the memory...Techpowerup and HT4U both show multi-monitor power use in their reviews.

At the same time?!? That's what I call multitasking!

All contemporary video cards support at least two screens. Even a five year old AMD motherboard with a Nvidia chipset that I've owned supports two screens. So you have nothing to worry about.