No. The 'Eragon' series has a large following for its story of adventure, magic, and friendship. Adding sexual content through fanfic is not in line with the general tone and values of the fandom. It can also make many fans uncomfortable.
One possible theme could be power. Since he has dragon's blood, it's likely that power - related themes such as how to control it, the responsibility that comes with it, and the temptation it brings would be explored.
In the official Eragon lore, we have epic battles, the bond between dragon and rider, and the exploration of a richly detailed fantasy world. But any form of sex stories are completely absent. The series is aimed at a wide range of audiences, including young readers, so it adheres to a certain standard of propriety.
Dongfang Shenwa was a Chinese web novel in which the Dragon and Phoenix were the main characters. Due to the complicated plot and character setting of the novel, it was impossible to determine whether the Dragon Child liked the Phoenix Child. In the novel, there was a complicated emotional entanglement between the dragon and the phoenix. Their relationship was sometimes close and sometimes distant. Whether or not they liked each other depended on the development of the plot.
I'm not sure which novel you're referring to, but "Oriental God Child" usually refers to an animated film rather than a novel series. If you can provide more information, such as which version of the "Oriental God Child" you are referring to, I can try to provide you with a more accurate answer.
In the 'eragon has dragon's blood fanfiction', it could be that the author is playing with the idea of how the dragon's blood affects Eragon's character development. For instance, the blood might fuel his sense of justice and make him more protective of the dragon race. It could also lead to him having to hide his true nature in some stories, which would add a layer of secrecy and intrigue. Additionally, this fanfiction might introduce new dragon - related lore, perhaps about ancient dragon bloodlines and how Eragon's blood ties into that larger mythology.