Animal Crossing: New Horizons supports the registering of up to 8 users on a single Nintendo Switch™ console with a single copy of the game, all of whom can share a single island.

Up to 4 inhabitants can play on the same island (but each player needs a controller).
Using local communication, up to 8 of you can get together on your own island or a friend's.

Even using multiple copies of the game, you can only create a maximum of one island per console. If you'd like to create another island, you'll need another console.

Yes, the game works on the Nintendo Switch Lite.
However, in order to enjoy multiplayer with inhabitants from the same island on the Nintendo Switch Lite (in Party Play mode), you will need a Joy-Con or Nintendo Switch Pro Controller for each player.

You can't change the Resident Rep during the game.
If you'd like to make a change, you need to delete the Animal Crossing: New Horizons save data and start the game again.
※Note that if you delete the Animal Crossing: New Horizons save data, it will erase all users' data.