People on Youtube say you can get into the house without playing the song of storms, which many people have done.
There is a way to get in. You place a bomb on the doorstep of the house and walk a little ways off. The little girl Pamela will come out when she hears the noise and if I recall correctly she should walk to the edge of the river. When her back is turned you can go inside the house.
Is the dad different if there's no river since the music box isn't playing?
No. You played the SONG OF HEALING, which healed him of being a mummy. The music box just keeps mummies away from outside the house.
And why inside the closet is he covering up everything in bandages like a gibdo because normal gibdos don't do that, right?
Like the teddy bear and stuff? I kind of get the feeling that his daughter did it. It could have been her teddy bear and she could have wrapped it up so it could be like keeping her dad company. Stuffed bears are like a comfort zone to little kids. It makes them feel better to cuddle something so maybe she thought that her dad would want it to help him feel better.
Hope this helps. :)