Miis do things like attempting to marry Miis based upon their relatives or Miis based upon their enemies, etc., them becoming best friends with the most unlikely people like their supposed enemies from where they came from, etc. They aren't meant to be the actual people - just their look-alikes. Which is why their sense of tastes, who they form friendships with and whomever they grow a crush on are all different than what one might expect from the real deal - they only look like whomever they're based upon. They're not the actual beings themselves.
The annoying item-dropping minigame and the ability to drop items out of the Mii's reach or throw them across the room can be thought to be a petty Cycle of Revenge between them Miis and the player: the player keeps doing the above so the Miis decide to pay back and annoy the player with the minigame, making the player more likely to annoy the Miis in a similar manner, or vice versa.
If you haven't been playing the game for a while, a Mii may greet you with something among the lines of "Have you been on holiday or something, [Your] look-alike?" which might not make much sense at first glance - if you're on holiday, you have more free time to spend playing the game, so why did they not say, "Have you been swamped with work?" Because the Miis know nothing about you but the fact that you own their island and have god-like powers. From their point of view, the game is your job.
You can buy your Miis an entirely new interiors, complete with new furnishings, and it takes almost no time to install. This makes sense, because the Miis are implied to be tiny enough to ride on a leaf! The interiors are basically like little dioramas- when you get them a new one, you can just slide it in in place of the old one like a shoe box.