It would be great to have the ability to change the component's parent menu and sub-menu item's 16px icons. And also have the ability to change the page title's 48px icons.

Each default icon is duplicated in a different name, so you just have to replace them in the images directory.
The best for the future will be a user personal icon library integrated in builder.
Already in roadmap.

About the labels :
The page label (next to the 48px icon) is took from the LAYOUT title.
It is the same than the menu item and the meta title.
If you want to modify the meta title of your component, you can add prefix and suffix in the main controller of your component. (first file called : mycomponent.php)

Thanks for your interrest and welcome to the community.