Yes. The only probably I've run into is "submitting scores" on games online. Not an issue. I have a tablet, have many of the Amazon apps on it and keep it offline almost all the time.
Yes, but it is NOT a big deal. Almost everywhere has free wi-fi. And odds are the Kindle will get so loaded with crap, that it won't even be an issue of not having another game/book.
Aircards are really pricey and come with a monthly fee. It is so not worth it. We've been everywhere, mountains of Virginia to the Dominican Republic and free wi-fi access is never a problem. It's always available somewhere. An aircard, unless you need it for business and have to be on the internet all the time, is a compete waste of money.