Well, in general, Shizuo is often depicted as the strong and hot - tempered one. In fanfiction, he might be shown as being very protective or possessive in a relationship with Izaya. Izaya, on the other hand, is usually the sly and manipulative character. In such fanfictions, he may use his wits to either get closer to Shizuo or drive him crazy. But remember, lemon fanfiction often has inappropriate content, so this is just a general view of how they are typically characterized in more appropriate fanfictions about them.
There's this fanfic titled 'Izaya - The Girl Among Them'. In it, Izaya being a girl makes her more of an enigma. Her actions and motives are different from the male Izaya we usually know. It's a fascinating read as it delves into how the other characters react to this new version of Izaya.
Celty might also interact with him. She's often involved in the events of the series. A drunk Izaya could be a source of confusion for her, or perhaps she would try to help him in some way, seeing as she has a kind heart despite her rather spooky appearance. Another possible character is Namie. Since she has a complex relationship with Izaya, she might be the one to find him drunk and have to deal with the consequences, whether it's covering for him or using his drunken state to her advantage.
Many female Izaya fanfictions have the theme of redemption. They might show Izaya as a character who is capable of change through his interactions with female characters. Or it could be the other way around, where the female characters are the ones in need of redemption and Izaya plays a role in that process. There's also the theme of the 'outsider' as Izaya often seems to be an outsider in the Durarara!! world, and female characters may share or oppose this aspect of him.
One possible plotline could be that Harry somehow gets transported to the world where Izaya exists and they form an unlikely alliance. Maybe they team up to solve a mystery that is plaguing both their worlds.
In the 'izaya gets drunk fanfiction', there are numerous possibilities. He might start hallucinating or misinterpreting events around him. His drunken state could also make him vulnerable to attacks from his enemies, since he's not in his fully alert state. On the other hand, it could be a chance for some characters to get closer to him and understand him better, as drunk Izaya may show his true emotions without the usual masks he wears in his清醒 state.
One common theme is the mystery around Izaya. Female characters are often intrigued by his complex and somewhat devious nature. They might try to figure him out, which leads to interesting interactions.
One common theme could be self - discovery. Since Izaya is a complex character, a female version might also go through a journey of understanding herself.
Yes, you can try Fanfiction.net as well. Look for tags like 'female Izaya' or related character tags. Some fanfictions might delve into the psychological aspects of Izaya as seen through the eyes of female characters. They could show his charm, his manipulative side, and how female characters interact with him, whether it's in a romantic, platonic or adversarial way.
I'm not entirely sure which specific 'Harry is Izaya fanfiction' is really good. However, you could also check out Archive of Our Own (AO3). It has a large collection of fan works. Maybe you'll be lucky and come across a great piece of fanfiction about this pairing there.