3.) Can I run my 5970 mining and game on my 560 Ti (1) is it possible (2) would it be laggy?
No, you can't.
This is because ATI computing goes through video driver. So Xorg must be loaded and running upon the ATI video driver. On the contrary, Nvidia computing doesn't need Xorg.
Wait what? Really? I started mining yesterday in a virtual terminal. I prefer to use a virtual terminal without x loaded because I feel (but am unable to substantiate) that running my miner without x loaded will free up resources on my card to be better spent on calculations. Is it really true that you absolutely must have x loaded to mine with an ati card? Does that really make buying an ati worth it?
I'm sorry. I miswrote it.
This is what I meant:
on Linux, Nvidia video driver and AMD video driver conflict. So you cannot load both. Mining on AMD cards requires the AMD video driver to be loaded: at this point, if you need Xorg (for gaming, for a desktop environment...), you cannot load the Nvidia driver, and you are forced to use the loaded video driver instead, which is the AMD one.
I haven't done it, but I've read that, on the contrary, you can use an Nvidia card for computation without loading its video driver. Nvidia computation doesn't need a video driver: so Nvidia doesn't need to "own" Xorg, if Xorg is there.
I hope I've been a little clearer, now.