Just finished it, love the graphics and gameplay. I haven't seen any story explanation but my take on this (spoilers ahead) is that the missingno monster is able to kill and replace other animals. I think the day you discover the corpse of the frog is the day it kills/replaces the bunny. Missingno can control multiple animals at once which explains the ending scene. A plot hole however is that in the day you go out by yourself for the onions you cant find the corpse of the frog, but when you go there the next day to discover it, it is implied that its been there for a while. Im probably wrong but this is just my take.
edit: maybe the missingno's ability also could be to turn other animals crazy, but that wouldnt explain the frog that has been dead for a while which was thought to be alive.