My Motherboard has 3 display outputs. Can I use 3 Screens?

The H67 supports 2 outputs: HDMI, and DVI-I. The VGA is a peel-out from the DVI-I and does not function independently.

Yes, depending on the OS.

According to the chipset specs, you can use up to two monitors with that motherboard using only the integrated ports. If you use all 3, I assume that one of them won't work, due to chipset limitations. If you use 2 displays, they, according to the specs, will not mirror unless they are set to, and will all work at the same time.

As for adding a video card with a vga output, on some boards/chipsets this will work and on some it will not. Some choose to disable the onboard video when a pcie/pci card is attached. YMMV. Considering that it's a new board, I'd say it'll most likely work.