I'm fairly sure those bars represent the guns ammo, given they don't seem to go down when moving.
Aye. Leaving aside that no one is taking four moves in a turn in spite of the heavier rifles coming with four bars, you can see the action economy bars underneath the person's HP bars when they're selected; they're the right-bracket symbols. Everyone except for the specialist loses one indicator per action as one would expect from these representing action units. The specialist's behavior is...odd, however. Their first move seems to be free throughout the demo, in that they don't lose an action unit, but if they, for example, move and then do something like throw a grenade, attack, or set up overwatch, they lose both action units on that second attack, and subsequent moves do still seem to take action units. If they don't take an action that eats an action unit (both the carry and call for extraction actions didn't show a cost), they can pull three moves in a turn. My assessment is that specialists might get one free move as part of their class features.
Also, I agree that the ease of terrain destruction did concern me a little, and while I think they're still fine-tuning the balance, I'm not sure that it isn't their intention to go that route to make it easier. They mentioned explicitly that there will be more destruction than ever, after all, and I'm not sure they were just talking about roofs and floors.