Yes, as long as you enter 1280x960 as the resolution.
No, the FOV calculation is based on the resolution you enter.
For black bars you should enter the native resolution of your monitor instead of the stretched resolution. I.e. enter 1920x1080 for CSGO as well.
Generally you do not need to touch it as the FOV Type is referring to how the game handles FOV, it is not related to your resolution or aspect ratio.