You are punished for changing the game time (no matter how much, it seems), but not the system time. Here's what happens:
If you change the time on your 3DS system, Animal Crossing seems to simply think that's the time it is now. Trees grow, events change, the only "bad" things that happen would have happened with the flow of time. Even going back in time via this method seems to work okay, even when going to a day previously played.
If you change the game time, using the option at the main menu of Animal Crossing, you will randomly trip for a while after changing the clock. The duration of tripping seems to last longer than the current play session, possibly the full day? But it eventually goes away. If, however, you were to change the game time this way before every play session you would trip randomly every single session, which is highly frustrating.
Also note that going backwards in time will spoil any turnips you had, since the game knows you went backwards, while it doesn't know you went forwards if you go by the system clock.
tl;dr: Change your 3DS's system time to time travel, do not mess with the in-game clock regularly or will will randomly trip.
Yes, they will. Villagers are able to move in on top of trees, bushes, etc. On the other hand, their houses are unable to spawn on rocks, PWPs or other houses. Villagers can spawn on fossils, but when they do so, the fossil is relocated to another part of the map.
(However, it is possible to "assign" the villagers a spot to place their houses. You can do this by leaving an empty plot in your village. Most villagers we like this spot and will thus build their house there. I cannot fully confirm this though.)
Best Answer
You can transfer your items, but not your house. The house is tied to a specific character, and can only be deleted by deleting the character. The items are not bound to any character, and can be picked up by other characters as long as they are not in your house.
If the character in question is mayor, you won't be able to delete him/her. The only way to remove the first character is to restart the town. You can transfer items to another copy of the game, restart the town, and transfer them back if you aren't too attached to your existing town.