As of now, in the manga, the identity of Luffy's mom remains unknown. There have been many theories and speculations among fans, but no official confirmation.
There could be an original character created just for the fanfiction. A woman with a kind heart but a tough exterior, who was a great fighter. She could have met Luffy's father during a battle and they fell in love, and she became Luffy's mother.
Happy might also become Luffy's friend. Luffy would be amused by Happy's flying ability and his cute appearance. Happy could also help Luffy navigate the Fairy Tail world, as he knows it well. And Luffy might share his food with Happy, which would make Happy very happy indeed.
She could be a former pirate captain herself. Maybe she was one of the most feared pirates in her time, and her skills and reputation were passed down to Luffy in some way, even if he didn't know it was from his mother.
Rebecca could potentially be in Luffy's harem. After Luffy helped her in Dressrosa, she might develop feelings for him. She is a strong - willed and kind - hearted character. Another could be Shirahoshi. Luffy has a special connection with her as he saved her from being captured. Her gentle and innocent nature would contrast with some of the other more assertive members of the harem.
Aside from Luffy, characters like Ace might show up in this type of fanfiction. Ace, being Luffy's brother, could have some connection to Luffy's discovery of conquerer's haki, perhaps through memories or some form of spiritual guidance. Additionally, some powerful enemies might be present. These enemies would serve as the motivation for Luffy to quickly master the conqueror's haki in order to defeat them and protect his crew. There may also be some minor characters from the One Piece world who assist Luffy in his learning process, like the inhabitants of a special village that has knowledge about haki.
Nami could also be a common character. She might help Luffy manage the financial aspects of his admiral duties, as well as use her navigation skills to assist in any navy - related voyages. And of course, she'd be there to keep Luffy in check when he gets too carried away.
Rayleigh would be a great candidate. He's an experienced pirate and has already trained Luffy for a while. He has a lot of knowledge about the world of pirates and could give Luffy a talk about the deeper secrets of the Grand Line or how to deal with the powerful enemies that lie ahead.