Vorkosigan Saga/WMG

Gregor had an older brother who died before the start of Shards of Honor.
If he were Prince Serg's oldest child, standard Barrayaran naming conventions would imply that he should be named "Ezar". He could be a second son -- Bujold hasn't written anything about Princess Kareen's family, so "Gregor" could easily be her father's middle name...
 * Possible, but I think it would have been mentioned. As a parallel to Aral's second-son-ship, at the least. Perhaps the naming after grandfathers is the custom among the nobility but not royalty, or custom in rural districts like the Dendarii mountains, or some such. It's unlikely to be a universal custom for the entire planet, at least.
 * Depends on how long ago the hypothetical elder son died. And remember that Ezar's pretty damn old. He's around Piotr's age. His children should be around Aral's age. Serg is very young to be Ezar's first child.

Ivan's going to marry a Galactic
He's about due another stint of embassy duty, and he's pretty much run through all of his prospects at home. Plus now that both Gregor and Miles have produced heirs, he's out of the crossfire, and being physically normal he's under less pressure to be conventional about such things.
 * The Amazon description of the next book heavily supports this, especially since it's about Ivan, and features him rescuing a female Galactic.
 * Confirmed. As of Captain Vorpatril's Alliance Ivan is happily married to Tej ghem Estif Arqua, a half-Cetagandan daughter of House Cordonah of Jackson's Whole.