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.

The Solstice Massacre was arranged specifically to discredit Aral Vorkosigan
By Grishnov, who as Minister of Political Education would be the logical person to be giving secret orders to the Political Officer of the Komarran Conquest. While Grishnov had likely not formalized his alliance with Crown Prince Serg and Admiral Vorrutyer by that time, he would be able to see even that far back that Admiral Vorkosigan would be his greatest potential rival for power among the men of his own generation. An Admiral Vorkosigan with an unblemished reputation as the conqueror of Komarr would have been an unassailable hero-saint to try and work against. By ordering the Massacre Grishnov forever taints the most prestigious accomplishment of his future rival with a truly blasphemous scandal and also guarantees that Komarr will be a source of great political unrest and strife... thus creating a 'permanent emergency' granting more power and authority to the officials in charge of the Empire's internal security agencies, of which Grishnov is among the foremost.
 * Parenthetically this means that Aral saved his ass without even knowing it when he killed the Political Officer. A counter-intelligence operative of that seniority would logically have been given the fast-penta immunity treatment, which would mean nobody could prove he was lying if he testified afterwards that Admiral Vorkosigan had given him secret orders. As Grishnov had almost certainly instructed the man to do.
 * A counter-theory is that the massacre was ordered secretly by Emperor Ezar Vorbarra, who would be essentially the only other person in the equation with the authority to issue secret orders to the Political Officer. However, this is far less likely for several reasons; while Ezar is more than ruthless enough to be morally capable of such deeds he was also smart enough to know that unrestrained brutality is not a magic cure-all for potential domestic unrest. After all, Ezar originally became Emperor over the corpse of Mad Emperor Yuri, who had died precisely because he had failed to take that lesson into account. Furthermore, Ezar is nowhere near careless enough to take out Aral Vorkosigan's reputation as collateral damage from a scheme. Had this been a plan of Ezar's either Aral's disgrace would have been a deliberate mission objective all along or the massacre would have been arranged under such conditions (such as after Aral had been 'recalled for consultations' or something) so that it could not possibly have been blamed on him. And not only did Ezar not want Aral disgraced -- he was, after all, the son and heir of Ezar's oldest friend and most reliable political ally as well as extremely important to the possible Vorbarra family succession in dynastic terms -- but if he had wanted Aral disgraced Aral had several true scandals from his youth, all neatly hushed up, that Ezar knew about and could simply have arranged to leak instead.
 * In addition to the simple fact that the logic behind the Solstice Massacre (rule by iron fist) was 180 degrees out from the underlying logic that Aral Vorkosigan had adopted for the Komarran conquest (rule as bloodlessly as possible)... and if Ezar hadn't agreed with Aral's plan for invading Komarr, he'd have appointed someone else to command the invasion.