Hi Graham,
Welcome back. I am doing great and hope the same for you.

1. Exactly same way as the normal WordPress/BuddyPress. The users are stored in wp_users table which is global among all sites of the network. BuddyPress simply provides(or overwrites) the way users register on the site.

2. No. But you should know that even if the users exist globally, they may or may not have a role on a sub site. Do you want the users to be assigned certain roles on each of the site? In that case, there are some solution that can be used.

3. It’s a good question. There are 3 choices here.

a) BuddyPress is only active on the one sub site. All other subsite’s won’t know that BuddyPress exists. In this case, you can simply activate BuddyPress on the 2nd site.

b) Network activated but to use 2nd site for social profiles/interactions etc:- In this case, add BP_ROOT_BLOG constant to your bp-custom.php (define(‘BP_ROOT_BLOG’, 2) ).

c). Want to have profiles on each of the site. In this case, we call it multiblog mode.
https://codex.buddypress.org/getting-started/customizing/bp_enable_multiblog/

From the description, It seems to me, either A or B will be better applicable in your case.

Thank you for being a valuable member.

Regards
Brajesh

Thank you Graham.
Please do let me know which approach suited you better.

For adding user to blogs, you may use

1. – to let users join a blog
2. Or you can auto add user to the blog they visit by putting this code in a php file and putting it in mu-plugins dir

/**
 * Plugin Name: Auto Add User to blogs
 * Version:1.0.0
 */
/**
 * Auto add user to a blog if they don't have a role.
 */
add_action( 'init', function () {

	if ( ! is_user_logged_in() ) {
		return;
	}

	$user_id = get_current_user_id();
	$blog_id = get_current_blog_id();

	if ( ! is_user_member_of_blog( $user_id, $blog_id ) ) {
		add_user_to_blog( $blog_id, $user_id, get_option( 'default_role' ) );
	}
} );

That will be automatically enabled across all blog and will add user to the blog they visit, if they are not a part of it. The last option is for role.

Hope that helps.

Regards
Brajesh

Thank you. I am going to look at it now.