Does gym class grouping go by age or by skill, or by both? Like, do they put 16 year olds with 8 year olds?

It depends on the gym - if they have enough people they will most likely do it by age and by level, but if they don't they will probably do it by level. So yes, 16 year olds could be with 8 year olds in a class.

^^There was one 15 year old with seven year olds once, she made it to team! I'm so proud of her for continuing to do what she loves, despite her age. At my gym, there are very loose age guidelines. The only one that we stick to 99% of the time is that you have to be five before moving from preschool to schoolage classes.