Yes. They should work together from now on.
Nope. After IVX, it would be impossible to reconcile.
They should not hate each other, but go their separate ways.
There should be mutant/inhuman hybrids and make their own team.
I think it could work with some of the newer and younger characters from both sides.
It's easy to say "Have a rational reaction" to mean "have the reaction that I would have" but it isn't accurate. If you read the Inhumans run that was part of the original Marvel Now set you see 3 NuHumans who do go to live in New Attilan and work with the Royal family named Inferno, Flint, and Naja. Each of these characters have very clear, very rational reasons why they end up doing so. They aren't brainwashed, they aren't idiots, they aren't crazy cultists. They are people who have a unique perspective and experiences that lead them to the rational decision to do so.
If there ever was to be any unification efforts, I think it would be crucial for it to be between people who represent their societies, not just their genetics. Inhuman society is one of the main things that keeps tyem from being "mutant wannabes" and not including this valuable distinction would only further this inaccurate stereotype.
Claremont has talked about fundamental differences he sees between X-Men and Avengers (the Avengers are the exclusive fraternity of jocks and the X-Men are the family of ostracized nerds who will welcome anyone as they are and despite their flaws). To me, the Inhumans are more like the Avengers - they see themselves as better than everyone else, especially the Royal Family.
Marvel editors have been trying to convince X-readers to read Avengers or whatever other books they've tried to promote for decades now and don't seem to understand that the appeal of the X-Men isn't that they are superheroes and the fundamental difference that Claremont saw in how he approached the X-Men. The problem is the appeal of X-Men isn't that they are superheroes or what they might symbolize, but the way they function that is unique.
The Inhuman Royal family is completely opposite of everything I like about X-Men, so the idea of wanting to read a book about them makes no sense to me.
I've always preferred the X-Men over the Avengers because they had to deal with the fact that they were different unwillingly and had to choose to be superheroes or not. The Avengers were/are usually scientists, soldiers, spies, etc. I like them too, but I think that they had more control of weather they want to be superheroes or not. Bruce Banner, Spider-Man, the Fantastic Four and other mutates couldn't really choose because they were accidents, but they are still different from mutants...
The Royal Inhumans are a part of a monarchy and live in a place that they don't really face a lot of(or any) persecution. I think that the NuHumans can be on the same page as mutants because they didn't choose to be different and they are average people, unlike the Royal family and the inhumans living on Attilan.
We don't know how the whole NuHumans thing will play out, but paraphrasing what Cyclops said in Schism (I think???), the mutants save lives and people remain afraid of them and hate them, while when the Avengers do the same thing, they are seen as heroes by everyone. This can be debatable though.