Advice on the itinerary

My partner and I will be in Fukuoka 24th Oct morning till 29th Oct morning and we planned to go to these following places.

Day1: Explore Hakata/Tenjin/Dazaifu
Day2: Overnight stay at Yufuin going via Yufuin no Mori
Day3: Head back Hakata via YUFU train
Day 4: Day trip to Kumamoto/Aso via Shinkansen
Day 5: Day trip to Mojiko/Karato Market

My questions are:
1. Does JR North Pass covers all these places?
2. Should I get 3 or 5 days pass?
3. How much are the tickets to Mojiko from Hakata per person (If I get the 3 days pass)

Appreciate in advance for any advice and suggestions.
Thanks!