I just started on single player (creative / no mobs), built a house and built a bell using a music pad. Every now and then it activates itself and emits a musical tone. So my question is, is it even possible that if I'm not even nearby, it will simply activate itself?
No, he can't just activate himself. Maybe there's a redstone signal nearby, which triggers this block of notes.
If it is not wanted it can be a bug when loading chunk… Try Mall to play the map on an older / newer version or just uninstall your Minecraft version and reinstall Mall
No, not exactly, otherwise it would most likely activate continuously or maybe only once.
Then it is most likely a bug with the chance what another user has already written.