Why does the game say "Hit the spacebar"?
It's a turn-based game. Hitting the spacebar at the end of your turn (when the button in the lower right corner flashes) tells the game that you're done with your turn.
It's a turn-based game, as opposed to simultaneous action, or real-time strategy.What are the "turns" it is taking?
What exactly do the warrior and worker do? Can they do the same things or only specific things each?
Each one does specific things. The warrior fights wars, explores and does MP (military police) duty under certain governments, keeping people content. The worker improves terrain, builds mines and roads, irrigates, etc.