Ah no, it was just meant to be the sound of an arrow piercing through something

Thanks a lot for adding this doujin :)

Im not 100% clear if the flans were just magically split parts of flan

Remilia seems to think Flan's personalities split into 4 by magic, but the end shows that, in reality, they came from another dimension.
That's how I understood it.

Small trivia: one of the Japanese word for feelings/emotions is 喜怒哀楽 which is made of 4 kanji, each individually meaning one emotion (joy, anger, sorrow, pleasure). As you have guessed, the 4 Flans match each of the 4 kanji.