In the movie, there's a scene where the dead princes attempt to pick up the ruby that the king used to initiate their race for the throne. One of them mentions that they think it's "giving a little" — as in, they may be able to physically affect it. If that wasn't just wishful thinking, it may have been deliberate; they'd need more force to actually move it, which would imply they wouldn't get it anywhere unless all the princes were dead, and they would thus need to somehow get it into the hands of another heir.
Of course Septimus was the one prince to go to hell. Aside from being the most overtly sociopathic (the others mostly give the impression that they're murdering each other out of self-preservation/because it's what they've been taught, and confine their targets to each other, whereas Septimus casually kills pretty much anyone in his way), he killed the bishop.
Why do all of Una's brothers like her, even though they've been trying to kill each other for years? Since the throne must go to a male heir, they didn't see her as a threat, and so could allow themselves to be affectionate towards her; plus, even if she did have a son at some point, they would have assumed that one of them would be king by then and her child would have no chance at taking the throne.
Why did none of the seven princes seem to have children of their own, despite all being well into adulthood and in a society where they are more or less required to sire their own heir? Well, given how cutthroat the royal family is, they likely realize any child they fathered would be endangered if they turned out to be a boy (if their brothers even waited to find out), so there was likely an understanding that none of them should try to sire their own children until their "claim to the throne was secure".
That would explain why their father is as old as he is. Like them, he must've waited until his claim to the throne to sire any children of his own.
In that regard, the movie narrating how Tristan and Yvainne would go on to have lots of children and grown grandchildren by the time they moved on to the heavens does give a rather lovely implication that Tristan was the first to end the tradition. If they don't have to fight tooth and nail for their claim of the throne, then it would be safe for their progeny to have children without fear of being assassinated and such.
Why didn't Una try harder to escape her captor all those years? Maybe because it seemed like an improvement over the family she'd been raised with! Also, she left Tristan at the Wall. Quite risky, if you think about it: the guard could have been frightened of the other side and superstitious enough to just think "oh no, no fairy changelings please" or "well, the child's from there, so it's their problem" and leave the boy lying there. Not to mention that Dunstan could have simply refused to take him (especially in the book, where he was married and Daisy was pregnant already at the time). But, was still less risky than letting Tristan be raised with someone from Stormhold, thanks to all his murderous uncles running around.
