That's a bit of distance. I'll give it a go. I can't tell you it's the best, cheapest, or fastest but this is how I would go about it. Take time: 86 Minutes Transfer: 1 Times Distance: 166.4 km Total:¥ 5,080(Ticket Fare:¥ 3,180 Seat Fee:¥ 1,900) Ticket ¥3,180 Unreserved Seat Fee ¥970 begin 08:10 HAKATA Station [ Departure track No.13 ] SHINKANSEN NOZOMI 12 [16 Min] 08:26 transfer KOKURA Station 08:33 [ Arrival track No.13 / Departure track No.7 ] Unreserved Seat Fee ¥930 [63 Min] through LTD. EXP NICHIRIN SEAGAIA 7 09:36 end KITSUKI Station via "HyperDia" then Taxi Fare About ¥1,720 ( 4.7 km / 7 minutes ) Two-person ride About ¥860 / person 3 people ride About ¥574 / person 4 people ride About ¥430 / person Kitsuki Station, Yasaka, Kitsuki-shi, Ōita-ken 873-0015, Japan to Harmony Land, ５９３３ Fujiwara, Hiji, Hayami District, Ōita Prefecture 879-1598, Japan via "japantaxi jp"

Yes they should be open all of December. I believe they host Christmas and New Years events leading up to those dates. You should email them for their December schedule since it is not on their site yet, I would bet they are closed on the actual holidays but open otherwise. I have seen other reviews where they have offered blankets on the rides when it is cold in December.

Yes, free of charge. "Their Website" /english/harmony/hl_guide/info.html

I know there's public transportation. Perhaps you might be able to find out at the Tenjin Station in Fukuoka. We drove from Fukuoka Tenjin to Harmony Land.