In V10, are members able to select a theme from a list of themes in their profile? I've been searching for an answer and some limited results indicate it is possible, but I haven't been able to figure out how to do it. Basically, I'm getting mixed answers.

Yes.

When editing themes in the Admin Zone, there is a "permissions" section. You can set which groups are allowed to use that theme. If more than one theme is available for a member according to their groups, then they will see an option in their profile settings to change the theme.