For example, say a particular enemy squad is hit, and the squad counter is replaced with a casualty and two fire teams. Does the original squad counter go "back in the cup", available to be placed again when resolving any future PCs (this is how I've been playing it), or is it set aside and no longer available?
They are available for reuse. I can add some clarifying language in the rules. The biggest issue is when you have different types of squads that are drawn randomly, putting them back in the cup can skew the distribution. In that case I would recommend setting them aside and then if the cup is empty then refill from the dead pile.