Your cards affect your own board during your own turn. Your production cards apply only to your own production. There is nothing that can affect another player's board. None of your cards' effects apply during another player's turn.
Any Available Slot: This includes the always-available slot.
Any Slot Occupied By Another Player: This is any occupied slot, except those occupied by your action tiles. This does not include the always-available slot, because it is never considered to be occupied.
In a four-player game, a slot occupied by you and another player does not count as a slot occupied by another player (because it is occupied by you). …