I'm amazed with the amount of rings the Duchess has. I had no idea they were so many. Thanks for sharing those pictures.
1st set of pictures:
At first I thought it was a garnet but looking at the earrings and necklace, probably you are right and it is onyx. I'm not sure if you are aware of how appropriate those pictures are for the moment: out Prince of Beira is going to turn 18 next 25th March.
2nd set of pictures:
Is difficult to say what the stones are. Aquamarines as you suggested? Emeralds? The other ring seems to have a dark stone (sapphire? onyx?) and a red stone (ruby? coral?).
3rd set of pictures:
Rock crystal? Maybe. Or Aquamarines. However I'm inclined to say topaz.