travelling in kansai area 15 nights

We are 2 old persons. This is our first time to visitJapan.
Our itinerary:
Arrival at Kansai airport 9 may in the morning.
We plan to use the train direct to Kyoto.
- Kyoto 5 nights. Day trip Kyoto to Uji.
- Nara 3 nights.
- Koyasan 2 nights.
- Osaka 1 night
- Himeji 2 nights
- Osaka 2 nights
- 24 May morning to Kansai Airport.

What we need to travel?
Which train pass? IC Kansai One card also be useful for using train and buses?
Your best advise for travelling Nara-Koyasan-Osaka. The Heritage pass/ card is only valid for 2 days (valid from Osaka?) and we stay in Koyasan 2 nights.

Do you have any sugestion to add an extra nice place to our itinerary?

Thank you very much.

Arrival at Kansai airport 9 may in the morning.
We plan to use the train direct to Kyoto.

If you want to reach around JR Kyoto station and don't move around on that day, Icoca and Haruka ticket will be the best deal. If you want to reach far from JR Kyoto station and do some travel on that day, Kansai Thru Pass might be better,

- Kyoto 5 nights. Day trip Kyoto to Uji.
- Nara 3 nights.

Without knowing the precise itinerary it is hard to judge. But in general IC cards such as Icoca will work best.

- Koyasan 2 nights.

Kansai Thru Pass or Icoca.

- Osaka 1 night

Icoca or Osaka Amazing Pass.

- Himeji 2 nights

Icoca and use JR and non JR trains: From JR Osaka to Himeji, JR is faster, but you might need to go to JR Osaka by non-JR trains (most probably Osaka Metro).

- Osaka 2 nights

Icoca or Osaka Amazing Pass.

- 24 May morning to Kansai Airport.

Icoca. You might go by JR or Nankai, depending on the place of accommodation. In any case, Icoca will work.

I recommend adding Miyajima (Hiroshima Prefecture) to your list, 1 night minimum and 2 nights recommended. You can cut back on stays in Nara and Osaka to accomplish this.
https://www.japan-guide.com/e/e3401.html