I'm not entirely sure if there's a specific 'Naruto father of Katsuki Bakugou' fanfiction. There are so many fan-created works on the internet that it's hard to keep track of them all. It could be a really interesting concept though. Naruto has his own set of values and abilities from the Naruto universe, and Bakugou has his distinct personality in My Hero Academia. Combining them in a father - son relationship could lead to some really unique storylines, like Naruto teaching Bakugou some ninja techniques and how that would influence Bakugou's hero training.
Bakugou in lemon fanfiction usually retains his explosive nature, but it can be channelled in different ways. For example, his determination might be shown in his pursuit of a romantic interest. He may also be portrayed as having a softer side that only a few get to see, especially in more intimate moments within the fanfiction.
One common theme is the development of an unexpected friendship. Given their different personalities in the original series, fanfiction often explores how they can bridge the gap and become friends or at least respect each other more.
Often, in 'uraraka x bakugou fanfic', there is a lot of emotional growth. Bakugou might learn to control his temper better because of Uraraka, and Uraraka might become more confident in herself. The fanfic uses their relationship as a vehicle for personal development for both characters.
Yes, there might be some out there. You can check fanfiction websites like Archive of Our Own (AO3). There are a large number of fan - created stories in the My Hero Academia fandom, and it's possible to find one with this particular pairing and plot. Just use the search function on the website and type in relevant keywords like 'Bakugou x Uraraka pregnant' to narrow down your search.
One common theme is friendship. Many fanfics explore how Bakugou and Uraraka can form an unlikely friendship. Despite their different personalities, they find common ground and support each other's growth as heroes.
A great way to develop their relationship is through shared traumas. Maybe they both had a difficult experience during a villain attack. They could open up to each other about their fears and insecurities during that time. This vulnerability would bring them closer together. Additionally, they could participate in a hero competition together. As they face tough opponents, they encourage each other and celebrate their victories, which deepens their bond.
The plot could be about Bakugou getting exposed to some sort of gamma - like radiation that gives him Hulk - like powers. He then has to figure out how to control it while still being himself. Maybe he accidentally destroys some things around him at first, and has to face the consequences. Along the way, he could team up with his friends to fight against villains who are now even more afraid of this new, super - powerful Bakugou.
No, it is not appropriate. Writing fanfic that involves nudity in a sexualized way about a character is unethical and violates the boundaries of respect for the character and the source material. It also may not be suitable for a general audience and can make others uncomfortable.
One popular Bakugou Katsuki crossover fanfiction might be the one where he crosses over with the world of 'Harry Potter'. In this kind of fanfic, Bakugou could be a new student at Hogwarts, with his explosive personality causing all sorts of chaos in the wizarding school. His Quirk could be seen as a unique form of magic there, and he might have to learn to adapt to the new magical environment while also dealing with the typical Hogwarts drama like rivalries between houses.