Can't find an answer to this...

In an engagement, if a unit deals tactic damage to a participating enemy unit (and places the corresponding focus token on said unit) does that enemy unit still get to strike (by placing its own focus token on itself), or is it considered exhausted before being able to strike?

Thanks in advance for the help.

The unit targeted by Tactics is considered exhausted. One can create a rather controlling deck, such as the early meta "Sith Control", by focusing on inclusion of units with Tactics icons. And remember that the targeted unit does not have to be active in the current engagement. So one can focus down the scary units on the back line or bury the high priority exhausted unit under multiple focus tokens! Further more one can target that pesky unit committed to the Force to swing the Balance if needed!

Say Twi'lek Loyalist was in an engagement with a krayt dragon defending. LS wins edge battle. LS player strikes with the Loyalist. Places the one focus on the dragon. Now does the dragon take an additional focus (two focus in all) because he is forced to because he's in the engagement? I don't think so but.....

No. Once he's exhausted, he can't be chosen to strike, and therefore he doesn't get to execute the three-step strike process (being chosen, being focused, resolving combat icons).