Shin-Imamiya, Ebisucho or Dobutsuen-mae, not Namba. Rapi:t and Airport Express both stop at Shin-Imamiya, and Nankai lists Tsutenkaku as 10 minutes on foot.
Umeda Sky Building belongs to the Osaka Station side, not Namba. JR from the airport reaches Osaka Station in about 65 minutes, then you walk past Grand Front.
Karasuma Oike is a detour unless your hotel is there. From Kyoto Station use Gojozaka; from Kawaramachi or Gion use Kiyomizu-michi. Kiyomizu-Gojo is a 25-minute walk.
Airport Line to Hakata, then Nishitetsu bus 46 or 99 to Hakata Futoh (Bayside Place). International Terminal arrivals need the shuttle to the subway first.
Yakuin-odori Exit 2, then a short bus or about 15 minutes on foot. Last entry is 16:30, so a late landing decides whether the zoo still works that day.