Travel Plan and Which Pass?

Q. Can you confirm japan rail pass is valid on those routes?

5Apr: Arrive Fukuoka Airport, move to Kumamoto (stay Kumamoto 2nights)
6Apr: Explore Kumamoto & Asi
7Apr: To Yufuin area (Stay Yufuin Onsen!)
8Apr: to Fukuoka (stay Fukuoka)
9Apr: To Hiroshima (Stay Miyajima)
10Apr: To Kyoto (stay Kyoto 3nights)
11Apr: explore Kyoto
12Apr: probably day trip to Nara?
13Apr: move to Kanazawa (stay Kanazawa 2nights)
14Apr: Kanazawa
15Apr: Kanazawa to Osaka (stay Osaka)
16Apr: depart from Kansai to UK

faq Here is the individual tickets price for your itinerary.

Day1: Fukuoka (Hakata) to Kumamoto: ¥5,190
Day2: Kumamoto to Aso (return): ¥4,360
Day3: Kumamoto to Yufuin: ¥7,360
Day4: Yufuin to Fukuoka (Hakata): ¥4,430
Day5: Fukuoka (Hakata) to Hiroshima: ¥8,900
Day6: Hiroshima to Kyoto: ¥10,990
Day7: explore Kyoto
Day8: Kyoto to Nara (return): ¥1,380
Day9: Kyoto to Kanazawa: ¥6,910
Day10: Kanazawa
Day11: Kanazawa to Osaka: ¥7,640
Day12: Osaka to Kansai airport: ¥1,160

Total Price: ¥58,320

All the above route are covered by 14day Japan rail pass: ¥45,100.
Please note you can only exchange your pass at JR Hakata station and need to purchase the single ticket from Fukuoka airport to JR Hakata station which will cost you ¥250.