One reason could be that he wants to experience a normal life. In the wizarding world, he is constantly in the spotlight as 'The Boy Who Lived'. At a Muggle school, he might be able to blend in and just be an ordinary kid for once.
Harry could take the girl to his favorite spots in the wizarding world, like Hogsmeade. He would have to be careful not to expose too much magic at once. They would interact with each other through sharing their different cultures, Harry's magical one and the girl's Muggle one.
One potential Muggle actress could be Carey Mulligan. She has a great range as an actress and could bring a lot of depth to the role of the Muggle wife in the fanfic. Also, Felicity Jones could be a good candidate. She has a charm about her that would fit well with the idea of being Harry's Muggle actress wife. It could be interesting to see how her acting skills would be incorporated into the story, like if she used her acting to help Harry in some undercover wizarding missions in the Muggle world.
Socially, it would be a big change. In the wizarding world, he has friends who understand the magic and the unique challenges that come with it. At a Muggle school, he'd have to make new friends and keep his wizarding identity a secret. He might struggle to find common ground with his Muggle peers at first, but over time, he could learn a lot from them and vice versa.
Well, it depends on the specific fanfic. Some fanfics do depict Harry as being famous in the Muggle world. They might have a plot where Harry's heroic deeds in the wizarding world are so extraordinary that they can't be completely hidden from Muggles. For example, if there was a large-scale battle between good and evil wizards that took place near a Muggle area, it could attract Muggle attention and make Harry famous among them. However, other fanfics may keep the two worlds completely separate and Harry remains unknown to Muggles.
Maybe it's a Muggle doctor. Harry gets injured in the Muggle world somehow and she takes care of him. She has a strong sense of compassion and a no - nonsense attitude. Harry is impressed by her ability to heal and her determination. Their relationship starts from that moment of care and grows into something deeper.
In Harry Potter and Merlin fanfics, a Team Muggle Resurgence could be really interesting. It might involve muggles suddenly developing some sort of power or resistance against the wizarding world's dominance. Maybe they start to use their own technology and knowledge in ways that wizards can't anticipate, like using modern electronics to disrupt magic or something.
There are several ways for Harry to be famous in the Muggle world in fanfic. He could be famous because of his unique appearance. For example, if he has a scar on his forehead that is very visible and has some sort of strange power that Muggles can sense. Also, if he gets involved in a magical event that has a big influence on the Muggle environment, like saving a Muggle city from a magical disaster. Additionally, if he befriends some Muggles and shows them some small magic tricks that spread like wildfire, he could become famous.
Well, there are several common themes. Firstly, the theme of discovery. The Muggle girlfriend discovers the magical world which is full of wonder and danger. Secondly, the theme of sacrifice. Harry might have to sacrifice some of his time in the wizarding world to be with his Muggle girlfriend. And thirdly, the theme of protection. Harry has to protect his girlfriend from the threats that might come from the wizarding world, like dark wizards who might target her because of her relationship with Harry.