How do I use it? I had a Mediator invite a Chocobo into my team, and then for the next fight, I equipped someone with the Monster Skill ability, but when I tried to use it in the following fight, there was no option. How do I use Monster Skill to teach someone friendly monster's abilities?
Monster skill has a wonky description, and a wonky use. The game says any monster within 3 panels from the person with it equipped, that is _incorrect_
Monster Skill works as such: You have a Yellow Chocobo on your team. You also have a human with the Monster Skill support ability. In battle, you never actively select Monster Skill - it is a passive ability on at all times. If you move your Yellow Chocobo directly next to your human with Monster Skill - that is ONE panel away from him, not up to 3 like the description says - your Yellow Chocobo will now have Choco Esuna as an ability to be used. So long as the Chocobo is within one panel from the human, it keeps that ability. However, once you move the Chocobo away from the human, then it can no longer use Choco Esuna. There is no way to permanently teach a monster their Monster Skill ability.
Nope, sorry mate. Monster Skill doesn't really have a whole lot of uses in this game, to be honest. There are a few handy Monsters to have it with, but you have to question whether it is worth it to sacarfice a Support slot for a character and bring a monster in in the first place. Usually, unless you are doing a Behemoth SSCC and are trying to beat Yardow Fort City though, it isn't too handy. It can be fun, though.
There are some weird skills out there to access, though. Like the Great Morbol, which gets the ability to permanently turn another unit into a Morbol, or the Wildbow, who can sacrifice himself (crystallizes, so you can't rez 'em) to give someone an extra level, or the Mindflare, who can take a level away from a unit.
Usually, Monster Skill as a whole is little more than a novelety. It can unlock some cool stuff, some interesting abilities that you can find esoteric use for... but all and all, it just isn't that good. Behemoths probably benefit the most from it, overall, but outside of them, it is really, really hard to justify sacraficing a Support slot for Monster Skill.