BuddyPress.org

Hi @sedmikraska You can use following code

function profile_visibility_subnav() {
global $bp;
bp_core_remove_subnav_item( 'settings', 'profile' );
}
add_action( 'bp_setup_nav', 'profile_visibility_subnav',999 );

@jamesmct I do not think BuddyPress have any current option to manage all pending membership for all private group at single location.

@sanusalim If you have added register page as a menu, you can hide using https://wordpress.org/plugins/nav-menu-roles/ via menu specific option.
Make sure you have disabled “Anyone can Register” from Setting >> General
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