In the manga, Ayato survives his encounters with Kaneki. The story doesn't have Ayato being killed by Kaneki. Their interactions are part of the complex plot but not resulting in Ayato's death.
One common theme is the exploration of their relationship dynamics. Given their different personalities in the original work, fanfics often delve into how they interact with and influence each other.
You can try searching on some popular fanfic websites like Archive of Our Own (AO3). It has a large collection of various fanfics, and you might be able to find some great kaneki x ayato ones there.
Ayato in Diabolik Lovers is often portrayed as confident and somewhat possessive. In Ayato x Reader fanfictions, his character traits are usually amplified. He's shown to be highly attracted to the reader and will go to great lengths to keep them close. His vampire nature also adds an element of danger, as he may struggle with his blood - thirsty instincts while being in love with the reader.
Ayato would likely become more possessive. Since Yui is carrying his child, he would see her as even more precious and something that belongs solely to him. He might be more affectionate in his own rough way, like constantly checking on her and being more touch - sensitive.
Unfortunately, Kaneki did die in the manga. This event was a turning point that brought about many changes in the storyline and the dynamics among the characters.