Well, it could be that the baby dragon has some special powers. Maybe it can communicate with Harry telepathically. This would lead to some really interesting adventures as they bond and learn from each other.
Well, Harry might use his magic to make the baby laugh. For example, he could turn the baby's rattle into a little magical creature that dances around. He'd probably also be very protective, like how he was with his friends at Hogwarts.
Maybe the baby dragon is a rare species. This would attract the attention of magical zoologists and collectors. Harry would then have to deal with the ethical issues of keeping the dragon or giving it to those who claim to study it properly. He would also need to consider the dragon's own well - being and freedom.
There could be all sorts of things. Harry might use his broomstick to fly around in zero - gravity inside the spaceship. Or perhaps the Marauder's Map could be adapted to show the layout of the spaceship and the locations of any stowaway creatures or enemies. Hermione could be researching spells to protect the spaceship from alien magic attacks.
If Harry Potter becomes a dragon rider in fanfiction, he could explore new magical places. Dragons can fly to remote areas. He might discover hidden magical lands or ancient magic that could help him in his fight against the dark forces. Maybe he'd find a new kind of magic that could defeat Voldemort once and for all.
In this fanfiction, Harry might face a lot of challenges. First, he has to figure out how to keep the dragon egg safe. Hogwarts has rules against having dangerous creatures, so he'd need to hide it well. Maybe he'd use magic to create a special hiding place, like a hidden chamber. Then, when the egg hatches, he'd have to deal with a baby dragon, which could be really difficult as dragons are powerful and not easy to control.
Perhaps Harry Potter talks to the dragon to enlist its help in finding a powerful magical object. Dragons are known to guard treasures. He could be on a quest for a Horcrux or some other important item. The dragon might initially be hostile but as they talk, it starts to trust Harry. Their conversation could involve exchanges about the power of magic, the dragon's own experiences in the magical world, and how they can both benefit from working together.
The dragon could help Harry in battles. For instance, in a fight against Voldemort's Death Eaters, the dragon's firepower would be a great advantage.
Well, Naruto might be really confused at first. He's from a world of ninjas and suddenly has to take care of a baby wizard. He'd probably use his ninja skills to protect Harry. For example, he could set up traps around the house to keep bad guys away. And he'd surely try to feed Harry some ramen, which might be a bit strange for a baby used to wizard food.
If Harry were a Dragon Animagus in the First Task, it would change the whole dynamic. He could use his dragon form to create a diversion. For example, he could make the real dragon chase him away from the egg, and then quickly transform back and snatch the egg. Also, his dragon form might have some special abilities like breathing fire in a controlled way to fend off the real dragon if it attacks.
He might gain the ability to breathe fire. Just like dragons, if Harry had a dragon's heart, it could endow him with some of the dragon's physical abilities.