as someone who has to reread this every time it updates, because they are just THAT far in between
yes, they have started dating officially.
they have had some conflicts, like hiyori wondering if hodaka actually likes him or if he just wants to eat him. hiyori wondering if hodaka will get tired of him. hodaka trying to prove that he does like hiyori for him but his instincts arent something that can be avoided either.
the prey-predator relationship is kinda the foundation of the story, but in the last few chapters after becoming official, hiyori is wanting to make their relationship more "normal" (also tying into hiyori wondering if hodaka will get tired of him). doing things that normal couples do, wanting to be intimate without "eating," just kissing, making out, touching, sex, without hodaka feeding on him.
overall, the story is pretty lighthearted, funny, and mainly based around their relationship as human and demon. most conflicts arent really framed in a dramatic or angsty way, more so comedic. hope this helps!
i haven't reread this but is there any plot besides the prey-predator relationship did they start dating did they have conflicts will they become college students or what,,,