If you do a normal plugin deactivation and deletion on the WordPress Plugins page for the BPS free plugin then none of your database options settings or files (BPS free plugin files are deleted, but /wp-content/bps-backup/ files are not deleted) are deleted and will still be saved when you uninstall BPS free. If you click the Uninstall Options option under the BPS free plugin on the WordPress Plugins page and choose Complete Uninstall then everything is deleted – all files and all BPS database option settings.
Yes, your Login page will be briefly unprotected since Login Security will not be active when you uninstall BPS free and until you install BPS Pro and run the Setup Wizard. This is really not something to be too concerned with since the whole process should only take a minute or 2. When you delete BPS free using the standard plugin deactivation and deletion steps then your website is still protected with htaccess file firewall protection even after deleting BPS free.