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...
Ivan's going to marry a GalacticHe'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.
Part of the reason that Simon went along with the plan to break into the vault beneath ImpSec HQ was because he was hoping they'd damage it somehow in the processHe'd hated that building for his entire career, and had been trying on and off to get the funding to replace it for thirty years before his efforts were ended by his retirement. If there was a chance he could finally get rid of that eyesore once and for all, then he was going to take it.
Kou's Wedding budget woes were solved by Lady Alys insisting on holding the weddings at Vorkosigan House, Vorbretten House, or the Imperial ResidenceGregor is likely to be a wedding guest after all, so the location has to be secure. And Lady Alys is the Emperor's social secretary and still owes a debt to Drou and Kou