The Raspberry is probably cheaper then trying to find a cheep Android mini PC but I'd go with the Banana Pi as it is faster then the Raspberry and I believe Wi-Fi is included.
No. It has ethernet but you'll need the $8 Edimax USB/WiFi dongle for WiFi same as the RasPi. BTW, there's a script available that allows you to configure the Edimax w/o having the ethernet connection live.