BuddyPress.org

You could put it in here:

https://codex.buddypress.org/themes/bp-custom-php/

@oliverrealize You can download from https://plugins.svn.wordpress.org/buddypress/trunk/buddypress.pot

@nebuchadnezzar no need to modify anything inside BuddyPress core files, You have to modify template files inside your child theme.

Copy BuddyPress folder from your parent theme and paste them into the child theme and modify inside child theme at following path

buddypress/members/register.php or
buddypress/registration/register.php

You can check following for reference

Template Hierarchy

duplicate thread https://buddypress.org/support/topic/new-user-login-not-working/

You can use your developer to create a widget to create a contact form using displayed user id email as a receiver. For reference, you can check https://codex.buddypress.org/developer/playing-with-the-users-id-in-different-contexts/

The $bp Global

That depends on where you’re using it. You could use a bp_signup_validate filter to check that a username has certain characteristics. But for profile fields or other places, you’d have to enforce it some other way.

Here’s an example of how you might disalloe long usernames:

add_action('bp_signup_validate', function() {
	if ( isset( $_POST[ 'signup_username' ] ) && strlen( $_POST[ 'signup_username' ] ) > 60 ) {
		$bp = buddypress();
		$bp->signup->errors['signup_username'] = 'Geez, your username is really long.';
	}
} );

Here’s another report of this with a suggested fix: https://buddypress.trac.wordpress.org/ticket/7704

You might looks at adding an email using the BuddyPress email system: https://codex.buddypress.org/emails/custom-emails/

Maybe you could use friend relationships for this. If the “friend” terminology doesn’t make sense for your use, there is a plugin that creates one-way relationships called “follows” https://wordpress.org/plugins/buddypress-followers/

If you are asking about bbPress, try the bbPress forum.

If you’re asking about removing the BuddyPress email verification step for new accounts, there are several plugins that do that:

BP Disable Activation Reloaded

BuddyPress Auto Activate Auto Login

It looks like your buddypress/members/register.php file is based on an old version of the template (that had the field description hardcoded in the template). You’ll need to remove this line:
<p class="description"><?php bp_the_profile_field_description(); ?></p>

in that file.

There is an issue with hotmail/outlook rejecting activation emails (See the fix here: https://buddypress.trac.wordpress.org/changeset/11862).

Otherwise, the best way to customize your emails is explained here: https://codex.buddypress.org/emails/

There’s a known issue with hotmail/outlook addresses that will be addressed in the next minor update. You can see the fix here:
https://buddypress.trac.wordpress.org/changeset/11862

That may be your issue. If not, please provide more information.

Those look like bbPress files, not BuddyPress as such.