A:Answer More than likely. But depends on the model motherboard.
PCI-E is pretty compatible across cards and motherboards. PCI-E 3.0 cards will work in 2.0 and 1.0 motherboards, and vice versa PCI-E 1.0 graphics cards will work in PCI-E 2.0 and 3.0 motherboards.
There are however plenty of GPU and motherboard incompatibilities out there, but my experience its not related to the version of PCI-E, usually has to do with the motherboard BIOS/Firmware. I would recommend finding the model motherboard you have (or system if its a system you purchase assembled), and either contacting the manufacturer or doing some searches on video card upgrades.