As far as I know, the player has an ethernet input (details on them here if, like me, you're a bit un-computerish), so no "wifi", but it will connect with a cable. The 560 model is basically the same player, but with the wireless add-on.
Yup, if the player and router are close to each other all you need is an ethernet cable. If not, you need a wireless 'extender' (and an ethernet cable).