Can't you select it from the launcher?
No, except in windowed mode. If the launcher doesn't run for some reason, you have to edit settings.cfg file manually and then run the game using Darkest Hour.exe
The minimum required resolution for the game is 1024 x 768 pixels.
I use 800x600 quite often for bugtesting (in case it hardlocks and freezes so I won't have to restart the computer), should consider reducing the minimum. 800x600 works fine.
I always play at 1280 X 800 which is the 16:10 ratio of my 24 inch monitor -- although I could go up to 1800 if desired. Is there some special reason for exactly 1280 X 768?
Not 1280x768 but 1024x768.
No reason at all, except for the fact that the game was designed to be played only on that resolution since HoI 1. In Darkest Hour you can play on bigger resolutions too as we implemented support for those.