1. Only returns the owner of the first unit in a unit group
Hi, it works on my map as attached regardless of the unit index in the unit group. See the trigger -> Squadron Strike Cooldown Reset under the File Bomber Precision Strike in the map as attached. Also, use the Squadron Strike Ability from the Orbital Command and see that the strike platform group cooldown works as intended for player 1 (Owner of the Strike Platform Unit Group).
Did you save the Unit Group Variable (Global) as a string in the Save Unit Group in the Data Table action?, then use it as a parameter for the Function?.
and assumes the unit group is made of units belonging to only one player.
Yes. That is working as intended.