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.
In some fanfictions, Sirius Black is sometimes portrayed as Harry Potter's real father. This idea might stem from Sirius's deep connection and loyalty to Harry, as well as his role as a father - like figure in Harry's life.
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.
Was his father's identity real? This was a rather complicated question, and it depended on how one defined " reality." If he was referring to whether his father's identity was explicitly mentioned in the novel, then the answer was no. In many novels, the identity of the father is not real but a fictional character used to drive the development of the story.
However, if it meant whether the father's identity really existed, then the answer might be different. In some novels, the father's identity was a fictional character created by the author rather than a real character. In this case, whether the father's identity really existed depended on the author's will.
Whether the father's identity really existed depended on the plot of the novel and the author's wishes.
Another possibility could be Draco Malfoy. Think about it. In some fanfictions, they might rewrite the relationships completely. Draco has his own complex character arc, and perhaps in this 'harry potter is not the father' scenario, he ends up being the father due to some unforeseen circumstances, like a misfired spell that alters the course of events related to parentage.
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.