Trains and Tickets in Osaka

This is my first time in outside of the country and heading to Osaka, I'v done a lot of searching online but still confused.

1.) I'll be ARR at Kansai airport at 22:40 on Mar 4,
I might took JR rapid or maybe Nankai express before 23:40 but "if I not make it in time is there any bus to took me to Namba?"
*My hotel is at Tenmabashi but I don't see any train that go there in time.

2.) I'll be stay fully in Osaka on Mar 5-6
My destinations are USJ, Osaka Castle, National Museum, Shopping Streets, Maybe an Aquarium, Which Train ticket should I buy? ICOCA, Osaka Amazing Pass 2Day, or any suggestion?

3.) my flight back home is on Mar 7, midnight
I might be wondering around the city but "where can I store my luggage?"My bag is 80x50x35cm (tall x wide x deep)

Thank you in advance.

1. It is better if you could stay a night near the airport.
If it is not possible, you could check the following option:

- Night bus from the airport to Namba:
http://www.kate.co.jp/pc/e_time_table/e_namba.html

- Bus from the airport to Osaka station, from there, you could take the taxi to Tenmabashi around 4.4 km:
http://www.kate.co.jp/pc/e_time_table/e_osaka_sta_tt.html#from

2. I am also planning 2 days in Osaka. I think that the prepaid card is the best option with your destination. Moreover, you could consider Osaka One-Day Pass (800 for weekdays and 600 for weekends).:
http://www.japan-guide.com/e/e4006.html

3. If I were, I would leave my luggage at the hotel. Because if you leave it everywhere, regardless, you have to go back to take it.

thank you very much, those links help a lot.