annoying “Confirm Form Resubmission” message

This is more of general form issue than wordpress specific, but basically you should not submit forms to the page from which they are loaded at. You should have a dedicate URL which handles for submission and then redirects to wherever it is needed (success page on completion, back to the form if failed, etc). You can use the admin-post.php end point for that, which operates in a very similar way to the more familiar admin-ajax.php.

To use admin-post.php you need to specify it as the action url, so your form element will be something like
<form method ="post" action="<?php echo esc_url(admin_url('admin-post.php'))?>" >

might be useful https://www.sitepoint.com/handling-post-requests-the-wordpress-way/