1. If Prophet Muhammad (salallaahu alaihi wasallam) ever allowed a thing once for a while and later abrogated it, can someone do that thing just once with the intention to act upon that instance of Sunnah and later stop, whether its mut'ah or method of azan or prayer etc?

2. When mut’ah was abrogated, what did the spouses do?

3. What is the difference between mut'ah and misyar?

1. Abrogation started and ended during the time of revelation and there is no more abrogation since there is no more revelation. After a law has been abrogated no one has a right to act upon that law, this applies to everything including mut'ah.[1]
2. I don’t really know but I think they were given the option of either continuing their relations or separating.
3. Regarding the difference: In mut'ah both spouses agree and know the time when their nikah will be invalid and when that time comes the divorce takes place automatically without even the pronouncement from the groom. This is not the case with misyar.[2]

References:

[1] Ibn Qudamah, Raudhatun-Nadhir, 257 – 267

[2] Ibn Rushd, Bidayatul Mujtahid, 110