I thought it was difficult when first watching because I never seen that festival,
but it was very easy to get all titles by simple search :)
English title is not official, it just translated.
護国の祈り Gokoku no inori (Guardians Pray)https://youtu.be/27vJGPjh0K8https://youtu.be/6FGZuzDCN_Y
(finale night .ver with Lantern)
縁むすびの巫女踊り En-musubi no Miko odori (Matchmaking Maidens/Mikos dance)https://youtu.be/5jtRZ6Bpo_Q
幸せの鈴 Shiawase no suzu (Happy bell)https://youtu.be/gC3Q1n6x1ns
This special bell is "神楽鈴/kagura-suzu",
it is used in most shrines Japan wide, it is not just in Gokoku jinja(shrine).
However, these 3 songs are used for this shrine.
Unfortunately, each singer name and full lyrics couldn't find.
Basic group dancing style is the same as 盆踊り/Bon Odori(Bon Dance).https://en.wikipedia.org/wiki/Bon_Festival
(except with lantern and bells)
This shrine has about 150 yrs history, but it has disappeared by atomic bomb during the WW2,
but these songs are sung around 20 yrs maybe,
and seems sound sources such as CD seems is no sale so it has only in the shrine.
Although there is an contact/inquiry form on the site of the shrine
but it is not for foreigners even if you can send a message,
I don't know you can get an accurate reply quickly or not.https://www.h-gokoku.or.jp/otoiawase/