It is possible but not recommended. BuddyPress already has member profile fields. You should use that and it is internally supporpted by buddypress, just make sure you enable the “auto-link” in the profile field while editing the profile field.
If you are open on exploring, the WPLMS theme has members directories built on react and they are well connected with BuddyPress profile fields, example : https://demos.wplms.io/members-directory/
In all PHP & Cookie based login systems you will most likely need to refresh the page from the server. It may happen that when you refresh once, the browser shows as cached version, to confirm just change the url by adding a url/?1 ?1 parameter in your url to force browser to consider it as a new request.
IF you are using version 4, this issue would not appear. The login system is built on JWT, so it happens instant without page loads and there is no nonce passed here, so you can cache your pages for eternity as static html and get better page loading time.
Another point to note, check your PHP version. The PHP version 7.4.2 has an issue with GD Library for JPEG images. Upgrade to php version 7.4.8 or lower the php version to 7.3
Most likely you have a plugin installed for sending emails. BuddyPress detects if the wp_mail hook is being used by some plugin and sends in the text version.
You can however override this. Simply add this PHP code in your child theme – functions.php
