Guild Wars 2

You level up in fractals reward level by doing difficulty levels equal to or higher than your own right?
Example: A reward level 9 player doing a difficulty level 10?

If you do level 9, being level 9, you will be 10 after. If you do 10, the same.

Correct. You will also only receive a reward of level 9 despite doing it at 10. Which means you need to earn the right for a chance at getting the rings to drop.

Doing any fractal level higher than your current one will gain you a personal ‘fractal level’ advancement.

Doing higher level fractals will not yield you better loot because your reward level is tied to your personal reward level (the lower of your current level and the level you are playing).

Doing a level 10 or 20 daily on a character with a personal fractal level 9 will yield a daily chest once, but it will be a tier 1-9 daily chest. Therefore, no chance for a ring.