Most likely, Gray Fullbuster could be the father. They have a close relationship in the original story, so it would make sense for him to be the father in the fanfic.
One possible plot could be that Juvia discovers she's pregnant and she and her partner, perhaps Gray, start preparing for the baby. They might face challenges like telling their friends and family, and also dealing with the changes in their relationship due to the upcoming addition to the family.
Yes, there are some out there. You can start by looking on popular fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'Gray Juvia Lockser' and then filter through the results to find ones that might have the kind of story elements you're interested in.
One common theme is the exploration of their relationship's deeper emotions. Since Gray and Juvia have a complex relationship in the original story, fanfictions often delve into their unspoken feelings. Another theme could be the power dynamics between them, considering their different magical abilities.
The world of Fairy Tail itself provides a rich backdrop for their relationship. With all the magic, adventures, and battles, fanfiction authors have a lot of material to work with. They can create stories where Gray and Juvia go on secret missions together, or where they face a powerful enemy that tests their relationship. All these elements combined make Gray Fullbuster x Juvia Lockser fanfiction highly popular.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). There are a large number of Gray x Juvia fanfictions there. You can also check out Fanfiction.net. Just use the search bar and type in 'Gray Fullbuster x Juvia Lockser' and you'll get a list of relevant stories.
In a 'Juvia Gets Drunk' fanfiction, Juvia would most likely interact with the members of Fairy Tail. She might start bothering Natsu, asking him silly questions like if he can really breathe fire while drunk. She could also interact with Happy, and they might get into some sort of funny exchange, like Juvia trying to teach Happy a new song she made up in her drunken state. And of course, she'll interact with Cana. Cana being the drinker she is, might find Juvia's drunk behavior either hilarious or relatable and they could have a long chat about different kinds of drinks.
The relationship can start with mutual curiosity. Naruto is curious about Juvia's magic and Juvia about Naruto's ninja abilities. They begin to exchange knowledge, which brings them closer.
Their relationship would likely become more serious. They would have to think about not just themselves but also their baby. There would be more commitment and responsibility between them.