Changing user edit form
To preface, changing the Drupal user edit forms is not the most straightforward thing to do (when compared to changing the templates for regular site's theme), but it is possible, just as anything else.  Firstly, are you currently using one of the stock admin themes (e.g. Seven)?  If so, you will need to sub-theme that, which is done in the same way as you create a normal theme, then you just configure your site to use that admin theme.  Then, you can override templates.  In the case of the user edit form, it will depend the level of customization you want to do to the form. If you turn on debugging (see https://www.drupal.org/docs/8/theming/twig/debugging-twig-templates), then you will be able to see the templates you need to override at the form and field level.  Of course, if you can do what you need to do with CSS or Javascript (and it's not too kludgey), that is something to consider as well to avoid the pain of having to mess with the generation of the actual markup.