QWhile hBP05-066[Shiranui Flare] is in my collab position, hBP05-016[Usada Pekora] used Arts and downed [Sakura Miko] with hBP03-107[35P] attached.
In this case, in what order are the abilities of hBP05-016[Usada Pekora]’s gift "The Strongest Goddess", hBP05-066[Shiranui Flare]’s gift "Winter Trip", and hBP03-107[35P] resolved?

ARegarding the order of resolution, rule-based processes (e.g. down resolution, etc.) are resolved first. Therefore, the ability of hBP03-107 [35P] is resolved first.
Next, abilities that the turn player resolves (such as abilities when played, etc.) are resolved, so the turn player may choose the order to resolve the abilities of hBP05-016 [Usada Pekora]’s gift "The Strongest Goddess" and hBP05-066 [Shiranui Flare]’s gift "Winter Trip".

QIf my opponent has no cards in hand, and my hBP05-035[Sakura Miko] with hBP03-107[35P] and hBP05-085[Mikodanye] attached is downed, in what order are the abilities of hBP03-107[35P] and hBP05-085[Mikodanye] resolved?

AThe player who played hBP03-107 [35P] and hBP03-107 [Mikodanye] will get to choose the order.

QDoes the Arts "Sunshine Girl" of hBP04-072〈Oozora Subaru〉count hBP01-126〈Troupe Member〉and hBP03-107〈35P〉as well?

ANo, they are not counted.

QIf my archive has no hBP03-107〈35P〉, can I use the Oshi skill "Are 35P Making a Comeback?!" of hBP03-003〈Sakura Miko〉?

AYes, pay the holo Power cost, add hBP03-107〈35P〉 from archive to hand if possible, otherwise resolve the effect with nothing else happening.