Can I use these cards to save a unit that’s already in its base? What about one that’s already exhausted? If I can’t recall it, do I still exhaust it?

Yes. You can save any unit that meets the description in the replacement ability’s condition. For Highlander and Unlicensed Armory, that’s any friendly unit. The actions you perform on that unit as a replacement are like the effects of a spell or ability; you’ll do as much as you can: heal the unit (if it’s damaged), exhaust it (if it’s ready), and recall it (if it’s somewhere other than its base). And yes, you exhaust the unit even if you don’t recall it; as per the above wordings, we’ve changed the “recall it exhausted” language to make that clearer.