I think if you don't book Regent air, you don't get the transfer - but I could be wrong about that.
That's awfully late. Most transportation links will have already shut down at that time. Trains will be on the verge of closing if not already - not that it's that easy to take luggage with you on the trains anyway. Your choices will likely be to take a taxi to your destination hotel (expensive considering the distance) or taking one of the shuttle buses (have storage for luggage under the bus) that go into town center ... but the only line open at that time will be the line going to Osaka station.
http://www.kate.co.jp/pc/english/english.html (the uppermost link)
Latest bus is at 11:20 PM and it does stop at the Hotel New Hankyuu. If your flight arrives at 11:05 PM, not sure if you'll make it though :(
http://www.tripadvisor.com/Hotel_Review-g298566-d302282-Reviews-New_Hankyu_Hotel-Osaka_Kinki.html Other option would be to stay at the airport hotel for the night which is a pretty decent hotel as airport hotels go.
http://www.nikkokix.com/e/top.html and
http://www.tripadvisor.com/Hotel_Re...ikko_Kansai_Airport-Izumisano_Kinki.html Masaki
