BuddyPress.org

To redirect your users to their friends activities page on login, you can use this:

function bpdev_redirect_to_profile( $redirect_to_calculated, $redirect_url_specified, $user ){
 
    if( empty( $redirect_to_calculated ) )
        $redirect_to_calculated = admin_url();
 
    //if the user is not site admin,redirect to his/her profile
	$url = bp_core_get_user_domain( $user->ID ) .'activity/friends/';

    if( isset( $user->ID) && ! is_super_admin( $user->ID ) )
        return $url;
    else
        return $redirect_to_calculated; /*if site admin or not logged in,do not do anything much*/
 
}
add_filter( 'bp_login_redirect', 'bpdev_redirect_to_profile', 11, 3 );

Snippet source: http://buddydev.com/buddypress/buddypress-trick-redirect-users-to-their-profile-on-login/

To add a home button to the main menu, use WP’s menu builder. But this doesn’t let you add a dynamic button going to EACH user profile, only to yours. You will have to code this.

See from here how to do this:
https://buddypress.org/support/topic/how-to-get-notification-count-code/#post-244069
You need to introduce this:
$url = bp_core_get_user_domain( $user->ID ) .'activity/friends/';