When are the Xbox Fanfest Trivia rewards typically given out?

Hello ! I'm Kris and I'd be happy to help you with your question.

I believe its around 48 to 72 hours. I would suggest if you have not received by next week, then contact Xbox Support

https://support.xbox.com/contact-us

It's not possible to merge accounts.

The crystal was given to some people who took part in FanFest trivia for the 20th anniversary.

Are you talking about the Microsoft points given out at Fanfest? There’s always freebies given out a Fanfest that aren’t given out to every gamer on Earth. People pay to be there, and fly from all over the world to attend, there are bonuses for being there.
There’s also freebies given out year round, like the free season of Dragonball Z given out during Anime month, or Crackdown 1 free for everyone last year. They don’t have to do this, but they do. Being grateful for what you have and what you get is the best
way to be, you and I are priviliged enough to have disposable income to spend on gaming, many people don’t even get that opportunity. Smile, laugh, and don’t sweat the small stuff.

P.S. It’s all small stuff.

Rewards are usually given out 4 weeks after the promotion ends. That said, it's run by a third party and mistakes do get made. I've not gotten rewards since last November, personally. However, this is not typical behavior.

You would need to contact Microsoft Rewards support via the contact link at the bottom of the Rewards site for further information. Typically they rotate out some rewards when they are out of codes.