He might be shocked. Naruto has seen a lot in his life, but seeing something new and unexpected in his son's eye could still catch him off guard.
Naruto could be proud. If the eye shows a sign of Boruto's strength or a unique ability, Naruto would likely be proud of his son's growth and development. He might see it as a continuation of the Uzumaki and Namikaze legacy. He would probably think about how far Boruto has come and how much potential he still has to unlock. Naruto could then start thinking about how to help Boruto further develop this aspect related to his eye.
It could also be that Naruto sees in Boruto's eye a sign of an emerging danger. The eye might hold a clue to a new enemy or a brewing conflict. Naruto, being the experienced ninja he is, would then start to take precautions and train Boruto more intensively to face whatever this sign in his eye indicates.
Boruto might be in awe. He has always known his father as the Hokage, a powerful and respected figure. Seeing Naruto's past full of struggles, loneliness, and determination would make him realize how far his father has come. It could also make Boruto more empathetic towards Naruto and perhaps inspire him to be more like his father in some ways.
Seeing Naruto's power in fanfiction can greatly influence Boruto's character. It could make him more determined to reach his father's level. He might start training harder and be more serious about his ninja duties.
Probably his time at the Ninja Academy. Naruto was always getting into trouble there, but it was also where he made some of his first friends. Also, his encounters with the Third Hokage could be shown. The Third Hokage was like a grandfather figure to Naruto, and their interactions were important in Naruto's development.
One common scenario is Boruto getting to see Naruto in a super intense battle, showing off his amazing jutsu. Another could be Naruto using his power to protect the village, and Boruto watches in awe.
Well, Boruto might have a range of reactions. If the fanfiction shows Naruto as a really powerful and cool hero, which he is, Boruto would probably feel proud. But if it's something that twists Naruto's character in a negative way, he would likely be angry or defensive. He respects his father a great deal, so any false portrayal could upset him. He may also find some of the more out - there or creative fanfictions amusing, like ones that put Naruto in a completely fictional adventure that's way different from what actually happened.
She might immediately go to comfort him. Hinata has always cared deeply for Naruto, so seeing him cry would likely trigger her protective and empathetic side.
He'd probably be in awe. Just imagining his dad with all that power would be mind - blowing for him.
Maybe it's the high expectations that Naruto has for Boruto. Naruto is a hero, and he might unknowingly put a lot of pressure on Boruto to follow in his footsteps. Boruto could be scared of not being able to meet those expectations.
Jiraiya would probably offer some words of wisdom. He has a lot of life experience, so he might tell Naruto that crying is not a sign of weakness but a way to let out pent - up emotions. For example, he could say something like 'Boy, those tears are like the rain that nourishes the seeds of your growth.'