Not really. 'Jessie's Girl' is a song that was likely inspired by imagination or a combination of various elements rather than being based on a specific true event.
Yes, there are likely many out there. You can start by looking on popular fanfiction websites like Archive of Our Own. Just search for 'Jessie Luke and Jessie kiss' in the search bar, and you should be able to find relevant stories. However, the quality can vary greatly, so you might have to read through a few to find one that really suits your taste.
Ash is usually very positive and determined. In Jessie's body, he might try to bring some of that positivity to Team Rocket, which would be a big change for them. Jessie, on the other hand, is more devious and cunning. In Ash's body, she might be more aggressive in Pokémon battles, using strategies that are a bit more underhanded at first until she realizes that Ash's way also has its merits.
James could be a potential character in Jessie's harem. They have a long - standing relationship in the Pokemon series, and in this fanfiction concept, it could develop into something more within the harem dynamic. Another could be Butch, as he is also from the same villainous group and might have an interesting relationship with Jessie in this new context.
For Jessie, you can develop her by showing her growth in terms of her relationships. If she's shy at first, show how she becomes more confident around Tony and the other Jessie. Tony can be developed by giving him a backstory. Maybe he has a troubled past that makes him more empathetic towards the Jessies. The other Jessie can be developed by highlighting her differences from the first Jessie. For example, if one Jessie is more artistic, the other could be more scientific, and show how they learn from each other.
One possible plot could be that Jessie and Luke are friends who gradually develop deeper feelings for each other. They might go through some adventures together, face some challenges that bring them closer, and finally share a kiss in a moment of realization of their love. For example, they could be working on a project and start to notice little things about each other that they find endearing.
In a fanfiction, Jessie's haircut could be the result of a bet. She loses a bet to Ash or one of his friends. As a forfeit, she has to cut her hair in a really outlandish style, like a Mohawk. At first, she's mortified, but then she realizes it gives her an advantage in disguises. She can now pass as a tough - looking punk trainer, which helps her and her team in their sneaky plans to steal rare Pokemon.
To develop the character of Jessie, start with her backstory. Decide where she came from, how she became a vampire. Maybe she was turned against her will by an evil vampire. Then focus on her personality traits. Is she shy? Outgoing? You can also show her relationships with other characters. For example, how she interacts with the kids she babysits, whether she's strict or more like a fun big sister.