I think I have found out why these were cut. On The Cutting Room Floor
, an epic website I frequent, they said that they might have been removed because of how creepy the scenes are. But, the idea would later be used in Twilight Princess where they could make a new character to show Link these skills.
Also, in the scene where he gains double health, I think Fierce Deity Link was originally supposed to just be what Link turns into when he gained double health, almost like he's wearing armor.
I don't understand why they used the Great Fairy for this though. I mean, there has to have been some other person willing to "teach" Link. I would've liked it if maybe some soldiers taught him, like in "Spirit Tracks".
The idea of training Link has been used countless games, but it just seems wrong in Majora's Mask.