Yes, you can play 1080p on this monitor.
Yes, you can play 1080p on this monitor.
Sorry, I don't understand IMO. The games you enjoy include GTA V and BF3,4.
In my view, games aren't that important since current ones support 16:10 and 16:9 screens. 1680x1050 is lower than 1920x1080, but the gap won't be noticeable when playing. Your graphics card handles 1680x1050 more smoothly, while 1920x1080 might cause black bars and a slightly blurry look. So in short, yes you can go for 1920x1080, but it's not necessary. I recommend sticking to your native resolution.