Tanist votes are never saved except mine: they are empty when I load the game

On your first question: disinheriting your heir is not possible unless you have elective succession. Then you change for example choose to elect your second or third son. Most of the time your vassals will elect the person you elect. Off course there is a chance they will elect someone else, so it's tricky.

On your second question: yes, it is possible. I have done it before (horrible me) when I was in kinda the same situation as you. My heir died relatively young and so his only son became my heir, but had really bad traits. So I plotted against my grandchild (who was about 4 years old) and managed to successfully kill him. There is a catch however, which happened to me. The plot was successful but the truth came out that I did it, so I got the Dishonorable trait and, even worse, the Kinslayer trait which gave me massive relationship penalty to my family and vassals. So yes, it's definitely possible but there are some serious risks.

You kill your own Duke. So long as the Duke's son (whichever) inherits his father's lands before his mother's there is no way you lose Jazira. The chance of the Duchess dying first is why you are getting the inheritance warnings. If she dies first there's a chance that her heir could end up inheriting Jazira as well when the Duke dies. With Orkney having Gavelkind succession, if she has enough holdings there's a chance both of her sons could be landed vassals of another realm when your Duke dies. If both sons are vassals of another country when the Duke dies, you'll lose Jazira for sure.

As Affine and Studoku point out, the reason your High Crown Authority isn't preventing this is because Jazira is not De Jure part of Byzantium. It only can prevent out-of-realm inheritance in the De Jure Empire. I don't understand why Primogeniture succession in Jazira would be giving the younger son Jazira while the older gets Orkney, that's just backwards. However, so long as the Duke dies before the Duchess, and before either son is landed, I can assure you the inheriting son (whoever that may be) will be your vassal.

I know you have said you don't care to have Orkney, but if you did, the solution would be to kill the Duke, then immediately begin plotting to kill the non-inheriting son. This would assure that Orkney went to the son that just became your Duke.

As you say, this is Crusader Kings. All things are possible through adequate murder.

If for some reason you wanted to achieve your goal without killing anyone (a strange concept, but bear with me): If you have a title to spare (even a barony will do) you can land the son that is the heir to Jazira. By giving him the barony, he becomes your vassal. When he inherits further titles those will also become a part of your realm, even if the titles he inherits from outside the realm are of higher rank than his first title. So long as he is landed in your realm, any lands he inherits become and/or remain a part of your realm.