Quick question: Do I have to control every soldier manually, or can I have a soldier act on his own? That is, shoot enemies, etc?

They have rudimentary AI.

Emphasis on rudimentary.

They're not too bad at digging for gold, so long as you start them somewhere safely underground and point them towards good deposits every now and then. Rocket AI is good enough for the job it needs to do, and your units have about an even chance against enemies, though it's not at all a reliable option for defense. They're probably working on it.

How do you leave them to act on their own devices?

Sentry mode, or if you feel lucky, Patrol.

Thanks for your patience. I've got one more question, though.

When you play Brain vs Brain, can one of the players be controlled by the computer?

Yes. It's called single player.

I thought that was basically the player fending off hordes of randomly spawning bad-guys on his/her own?

Brain v Brain = two humans facing each other. Because humans have brains, see.

He means playing against a bot but with a brain to kill.

Try death mode on Promgrounds. I say death because you can just waltz into the enemy base on any other difficulty.