To save user info on the same page by form submiting

I’m pretty sure you should add the page url (don’t hard-code it) under the form “action” attribute.

So assuming you have access to the_permalink(), you should do the following:

action="<?php the_permalink(); ?>"

Check if that saves into the $_POST array by adding the following somewhere in that file and try submitting the form:

<?php var_dump($_POST);?>