Okay, though let me know when there is something else I can give input on. I thought about the issue you were reporting with the units seemingly attacking before moving. This is generally caused by passing an action to the unit that is not defined in the name switch after AnimateAction. For BP_Unit_Anim any name not in the switch is immediately passed along to the animation blueprint. The default behavior of the animation blueprint is the attack animation. It seems that your two issues might be related, as passing undefined actions to the unit can also cause the action queue to halt, which prevents you from animating new units once the new turn starts (which is what you saw with the game being stuck in WaitForOngoingActions).
To update the ability box after switching weapons, queue the UpdateAbilityBox action in BP_Unit (and InitializeQueuedActions in the action manager if this is not called otherwise)