What happens to the Sabotage cards after you play them? Do they get discarded, never to show up again?
The rules say the cards are discarded (gone forever) unless otherwise specified on the card. And the only card that specifies otherwise is the neutral card.
Then does your Sabotage squad have to get closer and closer because you have one fewer card each time? (Page 9 Sabotage cards rules).
According to the rules, Yes.
What if both sides has units with the Sabotage specialization, who gets the neutral card?
The rules don’t seem to anticipate more than one nation having a sabotage specialization. None of the Fury scenarios have more than one nation with sabotage squads.
As an aside, I don’t personally care for this sabotage set of rules. In my opinion, it adds unwelcome overhead to the fine strategy card aspect of the game without really adding anything to the play. At least not anything that couldn’t be provided by mechanisms already in the game. Perhaps others will disagree.
The game publishers were clearly willing to add slightly to the complexity of TOI. As such, I believe introducing vehicle facing rules would’ve been less complex than these rules and would’ve greatly added to the tactical experience and play value of most scenarios. But I digress.