You can use Role to Role block feature. Please go to Front End PM PRO > Settings > Security > Role to Role Block
Set “From Role” as any role (except Administrator as you want admin to send message ), “To Role” as “All Roles” and “Block For” as “New Message”. This block other role users from sending new message (They can send message to admin, if you set that).

For changing order add following code in your theme’s (child theme’s if any) functions.php

add_filter( 'fep_menu_buttons', function( $menu ) {
    $menu['message_box']['priority'] = 1;
    $menu['newmessage']['priority'] = 2;
    $menu['announcements']['priority'] = 3;
    $menu['directory']['priority'] = 4;
    $menu['settings']['priority'] = 5;
    return $menu;
}, 50 );

I am sorry, had a typo in code. I have corrected it is last reply. please use that code.

To add a menu button with unique class add following code in your theme’s (child theme’s if any) functions.php

add_filter( 'fep_menu_buttons', function( $menu ) {
    $menu['cus_button'] = array(
        'title'		=> __( 'Edit', 'front-end-pm' ),
	'action'	=> 'edit',
        'class'         => 'fep-button your_unique_class',
	'priority'	=> 15,
    );
    return $menu;
});

You can use conditional
eg.

add_filter( 'fep_menu_buttons', function( $menu ) {
    if ( isset( $_GET['fepaction'] ) && $_GET['fepaction'] == 'message_box' ){
    $menu['cus_button'] = array(
        'title'		=> __( 'Edit', 'front-end-pm' ),
	'action'	=> 'edit',
        'class'         => 'fep-button your_unique_class',
	'priority'	=> 15,
    );
    }
    return $menu;
});