Rail Journeys

Hi,
I am planning to come to Osaka in October, and wanted to just make sure the following journeys can be covered on the JR rail pass (7 days).
From Kansai Airport into Tennouji/Imamiya (Using the Kansai Airport Rapid Service and/or express Haruka)
From Osaka to Oita, will most likely split this into 2 journeys. One to Nakatsu/Beppu, and then stay over then the following day to Oita, and the same journey back.
Then from Osaka to Kyoto - I am guessing any JR lines I can take, but probably most likely JR Kyoto Line.
And then back to the Airport.
However I am going for just a little over 7 days, (wont be arriving until very late Wednesday night, staying 7 nights, and then leaving the following Wednesday afternoon), but I am guessing it's best to get the pass to cover the first 7 days of the journey, so I can activate it from the airport? Does it count from hours it starts and count from there, or it counts from day from when it's activated? (Sorry if this is weirdly phrased). What would you suggest?
I imagine I will be walking mostly around Osaka itself, but also I can use my pass on any JR lines too?

Thank you.