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.
- Remember that Serg had a fetish for raping and torturing pregnant women. There may be very good reasons for why nobody mentions the death of an older sibling for Gregor, the same reasons nobody ever mentions any of Serg's other crimes anymore.

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.
  - As a side benefit, the conservative Vor lords would sooner put a mutant on the throne of Barrayar than a man whose elevation would mean they'd have a half-Cetagandan Empress who would bear quarter-Cetagandan Imperial heirs. Ivan has finally taken himself out of the succession entirely, and couldn't be happier about it.