The answer to 2 is yes. All DS' are region free, except you need a Chinese DS to play Chinese DS as it has a bit of extra ROM in it to store the language glyphs. Besides that, any game will play in any DS and you can play wireless altogether.
There can be some issues with some games when you use the Nintendo online service, as if you have, say, a US game it will want to connect to US servers, I think. I can't comment on this though, as my only online USA game is Clubhouse Games and I've not tried that online yet.
EDIT: The above problem will not occur with UK games and a US DS Lite as it's the games that fuss about foreign servers, not the console.