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.
There is indeed a certain order in which you receive the items, up to a point. Afterwards, you receive one of the previously awarded items randomly. The order is as follows:
First time: Nothing
Second time: Balloon
Third time: Balloon
Fourth time: Pinwheel
Fifth time: Bunny Balloon
Sixth time: Bubble Wand
Seventh time: Heart Balloon
Eighth time: Ice Cream
Ninth time: Soft-serve Ice Cream
Tenth time: Party Blower
More than ten times: Random item listed above
The color of the items you receive is random. You also can only Streetpass the same person every 8 hours to receive these gifts.
Additional Sources
Best Answer
Yes, it is possible to duplicate items, but only items that can be dropped on the ground.
That being said, I advise against doing it, because messing up the timing can corrupt your save file (making it unplayable) and it's obviously considered cheating.
If you decide to duplicate items anyway, here's how:
Sources: IGN guide, solidus snake777's GameFAQ