Luca first learns about the world and agrees to travel with Alberto because he wants to learn all of the interesting things that the human world holds.
Because this allows any audience to quickly acclimate to a new environment through the main character learning about their new surroundings, the fish out of water narrative structure is incredibly common.
In the end, Luca finds the courage to boldly stand in solidarity with his friend and be himself, even though it could mean forfeiting his hopes and dreams that might have been achieved through assimilation into human society.
Some of the references are small, such as a street sign in the background where Alberto and Luca first ask Giulia about the race.
Sitting on the floor at the foot of her bed is a small plush of Donald Duck.
Since Luca and all of the people who live underwater gently change into a human form upon becoming dry, it makes sense that there isn't any apparent pain involved with losing one's tail.