Yes, there are quite a few. You can start by looking on fanfiction.net or Archive of Our Own. There, you'll find various stories exploring the idea of Harry looking like Sirius, some might focus on how it affects their relationship in the wizarding world, or how it plays into the overall plot of the Harry Potter universe.
Fanfiction.net is a great place to start. It has a large collection of Harry Potter fanfictions, and you can use the search function to look for stories specifically about Harry looking like Sirius.
One popular fanfiction with Fem Harry looking like Lily could be 'A New Destiny'. It has an interesting plot where Fem Harry's resemblance to Lily plays a significant role in the wizarding world's perception of her. Another could be 'The Lily - like Harry', which delves deep into how this resemblance affects her relationships with other characters, like Snape who had a complex relationship with Lily.
It could be offensive depending on how it's meant. If it's said with a dismissive or negative connotation towards the idea of black - influenced interpretations or fanfiction in general, then it's offensive. Fanfiction is a creative outlet, and black - centric interpretations can add new and valuable perspectives.
Well, if fem Harry looks like Lily, it might lead to all sorts of new plot developments. It could influence how she's treated by certain characters who knew Lily, or even give her some of Lily's personality traits.
One reason could be Harry's impulsiveness. Harry often jumps into dangerous situations without thinking, and Sirius, being his godfather and having a protective nature, would shout at him to make him realize the risks. For instance, if Harry decides to go after a Death Eater alone.
He could be more defiant towards the authority figures he doesn't trust. Sirius was always a bit of a rebel against the Ministry when they were wrong. So Harry might openly question the decisions of some of the Hogwarts teachers or the Ministry officials who visit the school, if he feels they are being unjust, much like Sirius would have.
This is a rather strange and non - canon concept. However, in such a fanfiction, it might explore a very different magical world where male pregnancy is possible. It could involve a deep emotional bond between Sirius and Harry that goes beyond the normal bounds of their relationship in the original series. There would likely be a lot of drama and angst as they deal with the unexpected situation and the reactions of their friends and the wizarding community at large.
It would be very different from the original story. Harry's upbringing would likely be a mix of Remus' gentle wisdom and Sirius' rebellious spirit. There might be a different dynamic at Hogwarts as well, with his relationship to other characters being re - imagined.