Another challenge might be finding reliable sources to learn from. In Skyrim, there may not be many people who are experts in teaching Dragontongue, and the available resources could be full of inaccuracies or half - truths. Harry would have to be very discerning about what he learns.
One challenge could be the sheer complexity of the Dragontongue language. It's not like any language Harry has learned before. The grammar and pronunciation might be extremely difficult for him, especially since it's a language created for a completely different fictional world.
He could start learning Dragontongue when he's on a quest. For example, if he's searching for a powerful dragon - related artifact, and the only way to get more information about it is to understand the language of the dragons. So he has to find someone or something to teach him Dragontongue in order to progress in his quest.
One challenge could be the conflict between the rules of magic he already knows and the new principles of the Force. For example, the way spells are cast in magic is very different from how one might use the Force, so he has to unlearn some habits. Another could be the opposition from some of the more traditional Hogwarts professors who see the Force as something foreign and potentially dangerous.
One challenge could be the physical strain. The Harashin technique might require a different kind of chakra control and physical movement than what Naruto is used to. For example, it could demand more precise and rapid movements, which might be difficult for Naruto at first.
Well, for Naruto in this fanfiction, a major challenge would be dealing with the recoil of Raikiri. Since it's a powerful jutsu, it likely has a significant recoil effect on the user. Naruto would need to learn how to manage that so he doesn't get hurt every time he uses it. Also, in the world of fanfiction, there could be other ninja who don't want Naruto to learn Raikiri. They might try to sabotage his training, which would be an external challenge he has to face. And let's not forget that Naruto has his own unique fighting style. He would need to find a way to integrate Raikiri into his existing style without losing his edge in combat.
One challenge could be controlling the space - time aspect of Kamui. It's a very complex jutsu, and Naruto, who is used to more straightforward chakra - based attacks, might struggle to understand the intricacies of warping space and time.
One challenge would be Harry's strong will. He has his own beliefs and values that are opposed to Bellatrix's dark ideology. Another challenge could be hiding Harry from Voldemort. Voldemort might not approve of Bellatrix raising Harry in her own way. Also, Bellatrix herself has a reputation to uphold among the Death Eaters, and raising Harry could be seen as a risky and strange move.
One challenge could be the complexity of chakra control required for Particle Style. Naruto has always had a bit of a struggle with precise chakra control.
Another challenge is adapting his fighting style. Naruto's existing fighting style is based on his ninja training and the use of chakra. Ultra Instinct is a completely different concept. He has to figure out how to integrate the new power into his attacks and movements without losing his own identity as a ninja. For instance, he can't just abandon his signature Rasengan, but needs to find a way to use it in conjunction with Ultra Instinct abilities.
One major challenge would be understanding the magical world. Tony Stark is a man of science, and magic operates on very different principles. He'd have to learn about spells, potions, and magical creatures. Another challenge could be dealing with the wizarding community. They have their own traditions and laws, and Stark might find it difficult to fit in or make sure Harry follows all the rules. Also, protecting Harry from magical threats might be tough for Stark as his technology might not always work against magic.
One challenge could be getting the speed right. Flash Step requires incredible speed, and Naruto, while fast, has to adjust his normal speed to the extreme quickness needed for this technique. Another might be the chakra control. He has to learn how to use just the right amount of chakra to power the Flash Step without overdoing it and exhausting himself.