Arlinn, the Pack's Hope // Arlinn, the Moon's Fury

If you cast a spell with daybound during night, that spell will be front face up (that is, daybound face up) on the stack. However, it will enter the battlefield with its back face up (that is, with its nightbound face up). It won't enter with its daybound face up and then transform.

If Arlinn, the Moon Fury's second loyalty ability is making her a Werewolf creature and it somehow becomes day, Arlinn will transform, but the effect making her a Werewolf creature will continue to apply for the rest of the turn.

After Arlinn, the Moon Fury's second loyalty ability resolves, she is a Werewolf creature and not a planeswalker, so she doesn't lose loyalty counters when she's dealt damage.

Before a player untaps their permanents during the untap step, the game checks to see if the day/night designation should change.

Arlinn, the Moon's Fury's first loyalty ability is not a mana ability. It uses the stack and may be responded to.

If it is night, and the active player of the previous turn cast two or more spells during their turn, it becomes day.

Double-faced permanents with daybound transform to their nightbound faces as it becomes night. Similarly, double-faced permanents with nightbound transform to their daybound faces as it becomes day. This happens immediately and is not a state-based action. It happens any time it becomes day or night, not just during the untap step.

If it is day, and the active player of the previous turn cast no spells during their turn, it becomes night.