Most players don't bother to set up in-game time since it's accuracy was questionable for a long time. Also, unless a run involves time that isn't in-game, there isn't a need for in-time.

This is probably a bug and the mojang will need to fix the launcher, but I suggest making a backup of your saves folder, deleting .minecraft and the launcher, and reinstalling.

I agree, but it would be under ROM hacks/Mods like the Hypixel server parkour.