Hi!
First to check- are you playing non-beta? Beta has many issues in singleplayer.
Secondly- the game is structured mostly to play with a mouse, minimal keyboard.
Sounds like there are some issues with resolution, maybe. Any idea what resolution you're playing at?
Abilities generally are aimed like this:
[Ability button, e.g. Q] -> [Aim with mouse] -> [Mouse click to set the ability]
If you don't click, the cursor will follow you until you do, or right click/ESC to cancel.
The execute button switches to a '...' when the turn is executing. ('Planning' phase v 'Execution' phase). The planning/executing system becomes more clear when you start ordering multiple units simultaneously.
Also I think the word was 'triune', as in a trinity.
Let me know if you run into more problems! Sorry it's been a pain to play so far! -msb