I got a version of the zip archive awesome 5.6.3 pro
but I can't understand how to update it from 4.7 to 5.63 in veronika theme. Maybe you have some instruction?

There are detail instructions what to do directly on font-awesome page
https://fontawesome.com/how-to-use/on-the-web/setup/upgrading-from-version-4

After update, icons shows in category, but don't show in the admin panel. How i can fix it?

Admin panel is separated from front and require updates as well.

maybe you can show where it is?

Theme folder / admin

admin/function.php only in this file?

echo '<link href="' . osc_base_url() . 'oc-content/themes/veronika/fonts/fa/css/font-awesome.min.css" rel="stylesheet" type="text/css" />';
echo '<link href="' . osc_base_url() . 'oc-content/themes/veronika/fonts/fa/css/all.css" rel="stylesheet" type="text/css" />';
added a second line, but not icons, squares appeared