Which actions are turn ending under which circumstances?

1) All utility items (like medikits and grenades) are free actions, but you still need to have at least 1 action point remaining to use them

2) Most self-buffs like Axiom's Psych Up or Godmother's Overtime are free actions. There may be a counter-example but I can't think of one right now. Note that Adrenal Surge also allows Axiom to use Psych Up several times in a single turn to build up his rage (normally it's a free action but it still has a one-turn cooldown)

3) Actions that always end the turn (like Verge's Puppeteer or Axiom's Quake) should mention it in their tooltip. At the very least, there is a "WILL END TURN" yellow line in the description even when you're about to do it as your first action

4) Other actions cost 1 action point but do not automatically end the turn, so they can be used before or after moving for instance

5) Note that there is a weapon add-on called the Reflex Grip that transforms the act of shooting from a turn-ending action to a 1-action-cost one, meaning you can shoot and then move, or shoot twice. Similarly, auto-loaders make a certain number of reloads free every mission (1 for the basic version, and up to 3 for the superior one)

6) Some perks from leveling up or training can change an action's cost. For instance Claymore's Sticky Bomb is turn-ending when you first get it, but you can later make it only cost one action point.

7) Torque's Tongue Pull is a special case because she can always use Bind after pulling a target, even if she moved before doing it.

That should cover most of it.