You should not mix ATI based and NVidia base cards except under Windows 7. Depending on the number of PCI-E lanes you have available it should not aversely impact performance. It depends on the motherboard. This is assuming you are not using crossfire or SLI. Most cards support multiple monitors so you can drive more than one monitor per video cards. What cards are you looking at and which motherboard do you have?
Yes they can, but you're going to run into issues running separate DX/OpenGL apps in each. If you can get it working, you'll definitely notice performance advantages if the apps in question can max out a single card - if the apps dont max out a single card, you'll notice notice less of an increase. It should be noted that if the app is using less than 50% of the gpu power consistently, you will notice zero performance advantages with multiple cards.
I'm going to go out on a limb here and guess that you're looking to stretch a single game across multiple screens? The eyefinity thing will work - but you'll need to pay for it, only amd's high end cards support it right now. I'm sure nVidia will have their version eventually.
If thats the case, then you probably wont see any performance benefits of using multiple video cards.
Even if you have a game running in one monitor, and you're browsing the web in the other, you're not going to see any significant FPS loss in the game. Rendering 2D surfaces is trivial to a full speed GPU (meaning one that isn't down clocked due to no 3D apps running).
That said, it is possible. In fact, this is how multiple monitors were used originally, video cards never used to have multiple monitor outputs - you needed a card for each one.