I can only advise Day 1 there when arrive KIX, exit arrival hall into JR office, purchase the ICOCA & Haruka Express one way (2000 + 1600) = 3200 yen.
That's the cheapest rapid train from KIX to Kyoto, that I know.
ICOCA costs 2000 yen and consist of 1500 amount inside, can use at convenience store, transport, some restaurants, etc. Something similiar like TnG, HK Octopus, SG EZLink, etc.

Day 2, check the locations you want to go and the cost of bus/train. It maybe cheaper if use the IC card (ICOCA/Suica/Pasmo/etc.)

Day 11, check the Haruka express cost from Shin-Osaka / Tennoji / etc. to KIX. Should be 1600 yen as well. You can purchase at day 1 there.

Actually, personally think that you wont need any sightseeing pass, if you are only planning to go 2 places per day. From my experience, suica/icoca is more than enough to cover your daily expenses for train and bus.
For D2,D3, you can refer to regentcid taikor recommendation on the first page. In his itinerary, he already cover most of the foreigner tourist spots.

Then I would suggest must go places
1. Kiyomizu dera - must go cause they are going to shut down for renovation in 2017 March, and will only be opened in 2020 during Olympic

2. Kyoto station - Yes, Kyoto station itself you can spend almost your whole day there doing shopping, not to mention the ramen road in the 10th floor of the station itself, and it has very nice night view as well

3. Kamo river - If you love enjoy air breeze, then this is a must go places for you. Go for a walk during evening as you can enjoy a lot of street singer over there singing, dancing. Then after that you can go to pontocho to have a nice dinner meal

4. Arashiyama - this is a bit far in my concern, it takes around 30-40 minutes to reach there using keihan(maybe hanshin not sure the line name) line. Normal tourist attractions here, prepare to walk for long period if you plan to go to togetsu bridge

Hi! I want to ask about train transfer as shown below. At Keikyu kamata, there's only 2 minutes gap to change train (and 7 minutes gap to change train at Nihombashi). Is this doable? Is there any stairs involved when changing the train?
These are all last trains. If I miss any of this transfer, there wont be any next train and I will be stuck until the next morning.