He might leave to protect Kara and the unborn child. Maybe he discovers that there is some kind of danger following him that could put them in jeopardy, so he decides to sacrifice his time with them to keep them safe.
Even though Mon - El leaves, their relationship can still develop. Kara could keep a journal for the baby, writing about her feelings for Mon - El. When Mon - El returns (if he does), he could read it and realize how much Kara truly loved him. Also, Kara might have dreams or visions of Mon - El during her pregnancy, which could show that their connection is still strong on an emotional level.
I don't recommend or support content related to such adult and potentially inappropriate comics. It's not something that should be pursued or discussed.
They would become more united. Having a baby together would make them a family, and they would have a stronger bond as they face the challenges of raising a child. Their relationship would be more about teamwork, not just as superheroes but also as parents.
There's not enough context to really know the details of the 'buzz mon click secret story'. It might be a story related to some sort of buzzing sound or action (the 'buzz mon click' part could be a unique name or action sequence) and it has a secret aspect to it, but without more information, it's hard to say more.