They could have all kinds of adventures. Maybe they discover a rare Pokémon in a hidden forest. They might also meet some interesting characters along the way who teach them new battle strategies or share old Pokémon legends.
In Kanto, they might meet some trainers who mistake Serena as Ash's girlfriend. At first, it could be embarrassing for them, but as time passes, they might start to see each other in a new light. They'll have more time to talk, share their dreams, and support each other. Ash could help Serena become a better Pokémon coordinator in Kanto, and Serena could help Ash with his Pokémon training strategies. This mutual support will strengthen their bond.
In Alola, the new environment will bring them closer. They'll be exposed to different cultures and ways of interacting with Pokémon. This will give them more topics to talk about and more things to do together. They could attend local festivals, where they'll have fun and create memories. These shared memories will enhance their relationship. Serena might be more confident in expressing her feelings for Ash, and Ash might become more aware of his own feelings towards Serena as they spend time in this beautiful and exciting new place.
Maybe they get lost in a mysterious dimension where the rules of Pokémon battling and catching are different. They have to adapt quickly and find a way back to their own world while also helping the Pokémon in this strange dimension. It could be a place where Pokémon can talk, and Ash and Serena have to work with them to find an exit.
They might live in a cozy cottage near a Pokémon forest. Ash could go out every day to train and catch new Pokémon while Serena takes care of their home. She could also start a small garden with Pokémon - friendly plants. At night, they'd share stories about their day over a warm meal cooked by Serena.
One possibility is that they could explore the beautiful Kalos region together. They might visit all the different gyms that Ash didn't get to fully experience before. Serena could also introduce Ash to more of the local cuisine and they could have picnics in the scenic areas of Kalos. Maybe they'd even participate in some local festivals and make new friends together.
One idea could be that they embark on a new adventure in a region neither has visited before. They face unique Pokémon and challenges together, which strengthens their bond. For example, they might come across a rare Pokémon that is said to only appear to those with a strong connection. As they work to catch it, they realize their feelings for each other have deepened.
They might decorate their home with lots of Pokémon - themed items. There could be Pokémon plushies on the couch, Pokémon posters on the walls. Ash would probably have his trophies and badges on display in a special corner. Serena would add some nice floral arrangements to give it a homely feel.
In fanfiction, anything can happen. However, without specific details of the particular fanfic, it's hard to say for sure if Serena is pregnant. Some fanfictions might explore this plotline for the sake of drama or character development. It could add an interesting twist to the relationship between Ash, Serena and Lemon, but it also depends on the overall theme and direction the author wants to take the story.
They might have all kinds of adventures. They could explore the unique Pokémon in Alola. Ash would be excited to discover new Pokémon species and train them. Serena might be interested in the local culture and how it relates to Pokémon. Maybe they'll participate in some Alolan Pokémon contests together, with Serena showing off her skills and Ash cheering her on.