QMy hSD15-008[Juufuutei Raden] downed my opponent's hSD18-007[Mori Calliope].
In this case, do we resolve the ability of hSD15-008[Juufuutei Raden]'s gift "Twilight", or the ability of hSD18-007[Mori Calliope]'s gift "A Small but Special Present" first?

AThe turn player's abilities will be resolved first, so start resolution with the ability of hSD15-008[Juufuutei Raden].

QMy hSD15-008[Juufuutei Raden] downed my opponent's hSD17-008[Hoshimachi Suisei].
In this case, do we resolve the ability of hSD15-008[Juufuutei Raden]'s gift "Twilight", or the ability of hSD17-008[Hoshimachi Suisei]'s gift "A Song for Tomorrow" first?

AThe turn player's abilities will be resolved first, so start resolution with the ability of hSD15-008[Juufuutei Raden].

QMy hSD15-008[Juufuutei Raden] downed my opponent's hSD16-007[Sakura Miko].
In this case, do we resolve the ability of hSD15-008[Juufuutei Raden]'s gift "Twilight", or the ability of hSD16-007[Sakura Miko]'s gift "Plop Your Head on Miko's Lap" first?

AThe turn player's abilities will be resolved first, so start resolution with the ability of hSD15-008[Juufuutei Raden].

QMy hSD15-008[Juufuutei Raden] downed my opponent's hSD14-009[Shirakami Fubuki] with mascot attached.
Do we resolve the ability of hSD15-008[Juufuutei Raden]'s gift "Twilight", or the ability of hSD14-009[Shirakami Fubuki]'s gift "Can't Afford to Collapse" first?

AThe turn player's abilities will be resolved first, so start resolution with the ability of hSD15-008[Juufuutei Raden].

QWhen my hSD15-008[Juufuutei Raden] downed my opponent's holomem, when do I recover 20 HP with the ability of my gift "Twilight"?

AFor the down resolution of your opponent's holomem, the "if... downed" ability of hSD15-008[Juufuutei Raden] will be resolved first.
In this case, recover 20 HP to hSD15-005[Juufuutei Raden], your opponent archives their holomem, and reduces their life by 1. Your opponent turns it face up, and sends that cheer to 1 of their holomem.