Well, in the fanfiction, Iruka may be protective by constantly checking on Naruto's well - being. He could ensure Naruto has enough to eat, is getting proper training, and is not being bullied by other villagers. He might also be protective in the sense that he gives Naruto extra attention and guidance in his ninja training, more so than he would for other students.
It also improves Naruto's skills a great deal. He becomes better at combat and using his ninja techniques. For example, his Rasengan might be more powerful or more easily controllable after Iruka's training. Moreover, Naruto's confidence grows under Iruka's guidance. He no longer doubts himself as much and is more willing to take on challenges.
Physically, Iruka takes care of Naruto's symptoms. If Naruto has a cough, Iruka might make him herbal tea to soothe his throat. If Naruto has a fever, he uses cold compresses to bring the temperature down. He monitors Naruto's condition closely and adjusts his care accordingly, making sure Naruto is on the road to recovery as quickly as possible.
At first, it might start with Iruka showing simple kindness to Naruto, like making sure he has enough to eat. As time goes on, Naruto starts to see Iruka as a father figure. He looks up to Iruka and wants to make him proud.
It could be that he believes fanfiction sometimes goes against the intended spirit of Naruto. Fanfiction might include elements that he doesn't approve of, like changing the characters' personalities in a way that he thinks is wrong. For example, if a fanfiction makes Naruto overly mean or out of character, Iruka, who has a deep understanding of Naruto's true nature, would dislike it.
Iruka influences Naruto's early development by being a positive role model. Naruto looks up to Iruka and wants to be like him. Iruka's kindness and belief in Naruto give Naruto the confidence to start believing in himself.
Maybe in a story where Iruka adopts Naruto to protect him from various external threats and help him grow stronger in a more nurturing environment. This could lead to many interesting character developments and plot twists.
Kakashi could also be a common character. He is Iruka's colleague and they both play important roles in Naruto's life. In time travel scenarios, Kakashi might be involved in helping Iruka adjust to the time - shifted situation or they could work together on a mission that is affected by Iruka's time travel.