I wouldn't worry about it too much - the Physx present in BL2 adds little to the gameplay if anything. It has a poor implementation apparently which can hog resources iirc. I have to be careful with my 970GTX due to the 3.5GB VRAM thing :s
Hmm, I'm not sure. I've watched videos on YouTube and the addition of blood and particles flying about does make the game a lot better looking.
Does it make any difference if you play offline? Some posts in the GeForce forum suggest this might help. Others say it doesn't work properly post 600-series GPUs. But why newer GPUs should mess it all up, I have no idea.