what you need to do is talk to pally or pelly, and have the second DS card setup a certain way. you can read about it in the instruction manual.
you take over what's in your pockets, everything else in the town deletes/is like you were never there, i'm not sure to what extent.
your house payments might go away, again, i don't know the extent of the undoing.
i don't understand the second question.
you can't do it over wifi, it must be local. and you have to play your game on the second/other card, from now on. think of it as transferring your save file from one console (ds game card) to the other. your animal crossing character is the save you are transferring.