Nvidia And ATI in the same computer and running 6 monitors

Hello,

I have searched and searched the web but cant really find a question to my doubt...

I have a GeForce GTX 560 Ti and would like to buy a ATI HD7850-DC2-2GD5 wich has 2 dvi and 2 mini display ports wich in total allow you to have 4 monitors together

My first question is, can I have both cards in my computer? (windows7) and how does it work configuring the monitors in seperate softwares?! ati and geforce?! I have a little hard time seeing these work...

And my next question and most important, will I be able to run 6 independant monitors? (2 from my nvidia and 4 from the ati)

I know the ati eyefinity technology allows you to use 6 monitors as one big screen, but doing what I propose, will I be able to use 4 monitors as one big monitor and o0ther 2 independant?

Thank you so much for your help
And sorry for all the complex questions...