Depends. Like, my first few days here, when I didn't know where the library was, he'd drag me into following or... headbutt me. Whatever worked to get my attention.

[Which was... always fun.]

I doubt your moogle will do that.

Anyway, monster corpses can be used in brewing potions or their hides can turned into armor. And in some cases, monsters can be used as ingredients for food. Those are just some examples.