Yes, and it can be a lot of fun. But you should know the person before you let them into your village. Some people just try to ruin it for others and will come into your village and chop down trees or dig holes or mess up your game. Most game sites will have forums where you can read who is safe to interact with and who to avoid. But going to other peoples villages and having other people visit is half the fun of the game. After you visit somebodys village you can have the animals who live there move to your village and vice versa. Also anyone who ever visited their village can move to yours and they will reference where they came from. Also any constellation in the village you visit or anywhere they visited can appear in your sky. And if you connect to the wifi on certain holidays and dates you get special items from nintendo.

Yes, exactly. Interacting with other humans is a big part of this game, though certainly not a requirement (the game is plenty fun without it).

The part I found most interesting about it was seeing how other people decorate. In single player, you come up with a theme or style for your house, but it's really cool to see what other cool and/or crazy things other people have done with theirs. Same thing with the town. Interesting to see how people lay down tiles and plant trees to create this elaborate design in their town. Old fashioned cobblestone walkways lined with fruit trees. Pathways that lead you to the useful parts of town (like Tom's store). Seeing the people who not only managed to turn their entire town into a garden, but managed to grow an enormous quantity of difficult-to-grow, cross-pollinated species.

Absolutely. Each person needs their own gamechip though so they'll have a character to play with. Great game, my son's adore it.

My friend and I would exchange fruits by smuggling them in on a visit to the others' town. Since both of the main ones we grew in our towns were considered exotic in the other town, we were able to get a leg up in trading.
That was more playing with the another person though, not against. As far as I know, there's no direct competition in the game. We would have races to see who could catch the rarer fish first, and things like that. Fun game!