Aborting a three-way swap
a) If Bob aborts before step 2, then Alice will not reveal s. 6T will elapse and Alice will get her BTC back. If Bob aborts after step 2, then Alice will not reveal s, as she has no incentive to do so - only Carol is paid, so why would Alice reveal s and lose her BTC for nothing? Again the timeout is reached.

b) If Carol aborts before step 5, Alice receives the NMC, but Carol's payment times out and so Carol does not receive the LTC (and it is given back to Bob, who will, at the end of the protocol, have both LTC and BTC). However, Bob can continue executing the protocol and receive his BTC, so Carol aborting is only harming her. If Carol aborts after step 5, she will get her LTC payment. Alice has already received her NMC and Bob can continue executing the protocol to receive his BTC.

c) This does not make any difference in the protocol.

d) This would be a problem if Alice's contract expires in 6T, but both Bob's and Carol's expire in 4T. Alice could wait until time 3T has elapsed to claim the coins from Carol's contract. As soon as s is seen on the NMC blockchain by Bob and Carol, time 4T has elapsed. In this case, Carol can no longer claim her coins, as Bob's contract has now expired. Hence, the 1 LTC is returned to Bob. However, Bob can also claim the 1 BTC. So, in case Carol sees that Bob's contract has an expiration of 4T she should refused to create her contract.

e) In case Alice reveals s prior to step 3, Carol has not yet created the smart contract. If she is rational, she will not continue executing the protocol. If both Bob and Carol are rational, Bob can take the 1 BTC and Carol can take the 1 LTC. Then Alice is left without any money. Hence, Alice can only harm herself by revealing s early.

Maurice Herlihy has written a paper on atomic swaps involving multiple parties which I recommend.

PS: Typically, stopping execution in the middle of a distributed protocol is called "aborting", not "halting". The "Halting problem" usually refers to something else in theoretical computer science.