The ideal size for both heavily depends on your theme and the page templates it uses. There’s no magic numbers. The best way to add a message to the vendors would be to use the action wcvendors_settings_before_branding. Example might be:

function custom_wcvendors_settings_before_branding(){
    echo 'The best size for a banner is 1000x300px and the best size for a store icon is 200x200px';
}
add_action('wcvendors_settings_before_branding', 'custom_wcvendors_settings_before_branding');

That code in your themes functions.php file would take care of adding the text there.

You would go to wp-admin > Appearance > Editor and add that to your functions.php file. This is WordPress 101. If you’d like to learn more https://www.youtube.com/watch?v=XD6hGrZPkQU

Probably not, no. The resolutions *your* site wants is different than others. Different themes show things in different ways. The filters are there for when you need them, it can be easily customized. 🙂 There’s about 300 filters/actions in WC Vendors Pro, there’s tons of uses to extend and customize. =)