Thor's getting his eye back in the comics depends on the specific comic arc. Sometimes it happens as part of a major plot twist or a heroic achievement on his part.
In many cases, Thor eventually regains his hammer. However, the way it happens and the conditions attached can vary greatly from one comic series to another.
Thor typically gets his hammer back by demonstrating his noble character and commitment to justice. Sometimes, it involves facing difficult trials and showing that he has learned from his past mistakes.
Thor's hammer return in the comics happened when he overcame various obstacles, showed great strength of character, and reconnected with the powers that granted him the hammer in the first place. It was a complex and exciting storyline.
Perhaps Naruto is waiting for the right moment. He could be observing his classmates and the teachers in the academy to figure out who he can really trust. By holding back his power, he can better assess the situation and the people around him without revealing his full capabilities too soon. Also, he might not want to disrupt the normal order of the academy. Naruto might have a sense that if he goes all - out, it could cause chaos and that's not what he wants at this stage.
I'm not really sure specifically what the 'Hamdel Thor' back story is as it's not a widely known common tale. It could be a very specific or personal story, or perhaps a name that's not familiar in mainstream stories.