If you are counting, 1-based makes a lot of sense. If you're indexing, they're equally valid approaches. However, if you're indexing then you should be able to use an arbitrary range and not be restricted to one or the other (with a mapping function from your actual range to the language's base).

Yes, because the cart starts empty. But, more to the point, I don't call the thing I put into the cart that causes it not to be empty the zeroth item.