Which Pass will allow travel KIX to Namba

Is it possible to use the Osaka Amazing Pass / Osaka one day pass or any other to travel from the airport to the city center (Namba)?

Secondly what are the options for travelling from the city centre to Kansai Airport if you need to catch a domestic flight leaving 07:30 am?

http://www.japan-guide.com/e/e2357.html

Osaka Amazing Pass / Osaka one day pass don't cover the transportation from KIX.
Regarding the transporation in early morning, bus service is available from OCAT to KIX. Considering the departure time of your flight, the buses departing at 5:15 or 5:40 from OCAT may be the ones.
JR Line from JR Namba station is also available. The departure times at JR Namba station are 4:58 and 5:55. It takes 57 minutes from JR Namba to KIX station.

This might be a silly answer to your question, Yes... but Why? Here is the 2015 description of the Osaka Amazing Pass with the Nankai extension:

http://www.howto-osaka.com/en/ticket/ticket/others/osakaamazing.html

There is the Nankai private train that goes from Kansai Airport to Namba. This is included in the pass with the extension. The cost of just riding the train is either 950(45 minutes) or 1430(35 minutes) yen for a one way trip, and there is a 1000 yen ticket that lets you also use the subway once after arriving in Namba (look at the Kanku Chikatoku Ticket). Here is a link to the transportation page for Kansai Airport:

http://www.japan-guide.com/e/e2033.html

So why, if you are arriving, and only have a partial day on you arrival day, going to spend 2700 yen or so for a day pass? I am usually a bit jet lagged after my flight, and I don't think I would get the extra value out of getting a pass for the first day. My suggestion is that you just pay for the basic ticket, get to your hotel, and then spend the rest of the day walking around Namba.

I hope this helps.