QWith hBP04-037〈Ichijou Ririka〉's Arts "Oh? Wanna Fight?", I dealt 80 Arts damage, 50 special damage, and 30 special damage.
Can the opponent split the -30 damage reduction using hBP04-006〈Oozora Subaru〉's Oshi skill "Mental! Physical! Passion!" among the special damage and Arts damage during that turn?

ANo, they cannot.

QFor hBP04-006〈Oozora Subaru〉's Oshi skill "Mental! Physical! Passion!", if it is during the turn that the Oshi skill was used, can the〈Oozora Subaru〉which has yet to be dealt damage get -30 damage?

ANo, it cannot.
As the ability can only reduce 1 instance of damage, it can only reduce the damage at the timing that the Oshi skill is used.

QWhen my Oshi holomem is hBP04-006〈Oozora Subaru〉and my center holomem as well as 1 of my back holomem are hBP04-067〈Oozora Subaru〉, my opponent used hBP01-087〈Kobo Kanaeru〉's Arts "Rain Mantra".
If I use the Oshi skill "Mental! Physical! Passion!" when my back holomem hBP04-067〈Oozora Subaru〉is dealt 20 damage by the ability, can I -30 damage from the 40 damage dealt to my center holomem hBP04-067〈Oozora Subaru〉after that?

ANo, it cannot.
As the ability can only reduce 1 instance of damage, it can only reduce the damage at the timing that the Oshi skill is used.

QCan hBP04-006〈Oozora Subaru〉's Oshi skill "Mental! Physical! Passion!" distribute -30 reductions to both special damage from opponent's holomem and Arts damage within one turn?

ANo, it cannot.
As the ability can only reduce 1 instance of damage, it can only reduce the damage at the timing that the Oshi skill is used.