Shamim's Plugins

You can add 2 approaches
Suppose current user id is 2 (you can get that using get_current_user_id()) and connected users of this user in 2,3 and 4 (get that from your member plugin or using query)

Approach 1. You show only connected users in auto suggestion and in directory.

add_filter( 'fep_filter_rest_users_args', function( $args, $for, $q, $x ) {
	$args['meta_query'] = [
            'include' => [2,3,4], //Get ids from member plugin
        ];
	return $args;
}, 10, 4 );

Approach 2. restrict user from sending message to only connected users

add_filter( 'fep_current_user_can', function( $can, $cap, $id ){
    if ( 'send_new_message_to' != $cap || ! $can ) {
	return $can;
    }
    //Get ids from member plugin
    if( in_array($id, [2,3,4] ) ){
        return true;
    }
    return false;
}, 10, 3);

I see somehow PREFIX_fep_messages table is missing. I need administrator access to your website. You can provide me in https://www.shamimsplugins.com/sensitive-information/ or join https://meet.google.com/vuv-bawq-sxj at 4:00 PM (UTC) time (20 minutes from now).

You were too much behind, recommended to update regularly.
Please let me know follwoing
1. Does your DB user have permission to ALTER the DB tables?
2. Can you check in DB if PREFIX_fep_messages, PREFIX_fep_messagemeta and PREFIX_fep_participants tables exists?

Can you check in https://www.shamimsplugins.com/account/ that your website is listed correctly under your license?
If not you can deactivate license and activate again.

Let me know

You can use following code

add_filter( 'fep_form_fields', function( $fields ) {
    $fields['message_content']['type'] = 'wp_editor';
    return $fields;
});

Please go to Dashboard > Front End PM PRO > Settings > Emails > Email Sending Interval and change to any other value and save changes. Wait selected amount of time and check again.
Let me know.

For groups, all users need to be added to that group. And they may see other users message which is not sent to them.
Better add other users to that conversation so that they can see only that conversation.

Eg. You can add following code in your theme’s (child theme’s if any) functions.php, change $your_extra_user_ids values

add_filter('fep_filter_message_before_send', function( $message ){
    $your_extra_user_ids = array( 1,2,3 );

    //Only for parent message
    if( empty( $message['fep_parent_id'] ) ){
        if( ! is_array( $message['message_to_id'] ) ){
            $message['message_to_id'] = array( $message['message_to_id'] );
        }
        $message['message_to_id'] = array_merge( $message['message_to_id'], $your_extra_user_ids );
    }
    return $message;
});

Please follow https://www.shamimsplugins.com/docs/front-end-pm-pro/getting-started-2/only-admin/