Yes. The normal time is around 75 minutes from KIX to Kyoto but those early morning trains run on the same tracks as the commuter trains and make a couple of extra stops. The same trains go to Osaka as Kyoto, it is all one line that runs through Osaka on the way to Kyoto. The time to Osaka varies by which station you want but will be 35 to 45 minutes. There are cheaper trains to more interesting places in Osaka if you choose to go there. Try Hyperdia for Namba or Osaka Station.

You really don't have any choice but to wait until you get to KIX to buy your ticket to Osaka or Kyoto as there is no easy way to purchase in advance from outside Japan.