Sounds like something went bad with your install. What you should do is uninstall the game (including the game user profile files) and reinstall with the latest or near-latest install. If you want a 3D Geoscape with working night/day, get revision 29004, if you're happy with 2D Geoscape, get the latest one.
You can change the keybindings by going to the user profile folders and modifying the keys.cfg file. The syntax is easy and you can find more information and links in one of the FAQs.