Responses
For the ex-husband I'll just say he's probably acting to avoid suspicion. They don't have proof he killed Diana and accusing him or even getting caught investigating him would be a quick trip to the gallows for treason. The man is just doing his job like retail employees do; smiling and doing what they're told.
FL is the most washy. But the 3rd prince was young enough to not have been a major mastermind when Diana died. He also ran away from home for years and didn't want to go back, so he's a kindred spirit to FL. The king is the sussiest one so I expect that plot will come up now that she'll be around the palace more.
I don't mind them being all chummy with the fugitive prince but the ex-husband's enthusiasm in following the emperor's orders is kinda weird given how at first they seemed to dislike the royal family, and it almost seemed like they lowkey suspected they might even have been behind the first duchess's death?? If that's not how it went, then the artist's skill to transition a change in conversation between unrelated different topics really sucked...