Some units cards (and possibly other cards) have actions that can be played for a certain amount of resources. How many times can they be played per turn? I assumed it was once. But then I've noticed other actions that include the text, may only be activated once per turn. So I'm starting to think the unrestricted actions can be activated indefinitely, as long as the conditions are met.

Yep, unless limited by text, as many times as you have the resources to fire it up.