Since there is no boot screen for GTX570, so I still need using Ati 6870 for installing Lion, rite?
You can go straight from SnowLeopard to Mountain Lion, but I guess it depends on how you're installing it. Probably easiest to install with an EFI card and then switch, I was just pointing out that the installer works with the Fermi and Kepler cards out of the box.
As you stated don't install nvidia driver for mountain lion, do what does it mean by "running lion with the driver from nvidia"?
Since there is no boot screen, and if there is no other osx in other hd, there is no way to install mountain lion with GTX570, rite? I still need to use ati flashed 6870 to do the os install, rite?
How are you installing the OS? Do you have a DVD or some other physical media? If so, you should be able to install Mountain Lion with the GTX 570 card. If you have access to an EFI card, then yeah, it's probably going to be simpler to install ML with that card and then switch afterwards.