answered:
in the dark world, chara’s reflection shows them as they were before they died.
chara’s whole goal/drive is to go back to the days where they were still close with asriel, as now asriel doesn’t return their calls and travels the world all the time. (he’s a big time celebratory and the monster king)
feylow’s home has a mirror for a door. inside, therefore, chara looks like their reflection