No, it's not a popular genre. Most Harry Potter fanfics tend to focus on more traditional themes like his adventures, relationships with friends and enemies, and his growth as a wizard. The idea of Harry giving birth in school is quite unusual and not something that appeals to the general fanfic - reading audience.
Definitely not. Popular Harry Potter fanfic genres usually revolve around the magic, the battles, and the complex relationships within the wizarding world. A 'Harry gives birth in school' dating fanfic is very far from these common themes. It's a very niche and probably only appealing to a very small subset of fans who are into really out - there concepts.
Hardly. The mainstay of Harry Potter fanfic is centered around the elements that are prominent in the original books, such as the fight against Voldemort, the development of Hogwarts, and the friendships and romances that are more in line with the overall tone of the series. The 'Harry gives birth in school' concept for a dating fanfic is so far removed from these typical areas that it's not likely to be a popular genre. There may be a very few fans who might be interested in it for its sheer novelty, but in general, it's not something that has a large following.