Q&A

At the start of the turn, time moves forward by the clocks of the cards set that turn, including Compass Clock (Hunch Gray) and The egocentric password“ ”, and effects are resolved starting with the cards played by the priority player (the player on whose side the medal is after time has moved forward).
For example, if the player who played Compass Clock (Hunch Gray) is the priority player, "Return to the time at the beginning of the turn" is resolved first, then The egocentric password“ ”'s "Set the clock to midnight", so the Chronos ends up at midnight.

Yes, it does.
Compass Clock (Hunch Gray)'s effect moves the Chronos back after it has moved forward, so whatever the order effects are resolved in, it has changed from day to night once.

It undoes the clock moved this turn.
First, time moves forward by the cards newly played from hands at the start of this turn. Then, at the character/enchant/area enchant effects step, the clock goes back to where it was before time moved forward that turn.

Yes, NIRA-CHAN (Kan Saete Kuyashiiwa)'s effect can move the clock.
The effects are resolved in this order:
① Compass Clock (Hunch Gray) moves the clock back to where it was before time moved forward that turn ② NIRA-CHAN (Kan Saete Kuyashiiwa)'s effect moves the clock forward by 0 to 5 more.