Mega Houndoom would've been much more fitting as Lysandre's main Pokemon (in the final battle). The Fire aspect to represent "Flare", and of course "Dark", because like any villainous team, they're portrayed as "evil". I would've rather no Mega Gyarados at all then the poor design and nonsensical typing. Until (or if) something like you said happens (Mega Milotic part Fairy) I won't find much sense in Mega Gyarados as a Mega, no matter how descriptive GF is with their explanations.
Well, three times, I think, but only one of her appearances lasted more than two seconds.
There's only one point in the game you fight Trevor, and that's on the bridge before Snowbelle, I believe. You fight Tierno (or whatever his name is) once or twice, and, uh... I don't recall any battles with Shauna. I could be wrong. Rivals don't always have to be friends, but that's been the trend est. Gen III. Hugh was probably the closest thing to a "non-friend" rival we've got since then.
Just personal preference. His personality (at the time) seemed like it as catering to a specific audience (being particular fangirls).