2560 x 1440 Is actually 1440p.
1920 x 1080 is 1080p.
Yes. A 1440p display has more pixels, so it produces a much more sharper image quality. It also gives you more workspace when editing. You can preview your video in 1080p without using up your entire monitor.
I'm not sure if a 2k display is worth getting, but I'm definitely getting a 1440p one.
Gaming on 1440p requires more Vram. I've heard you'd need to turn up some settings down in order to enjoy a good 30 fps+ on a 970.