Shamim's Plugins

You were correct in interpretation of the problem. I also did the same but could not reproduce this. in screenshot-2 your line breaks are stripped out but in my test i cannot reproduce this. This means may be some plugin and/or theme code is changing its behavior. Can you please disable all plugins except this and change theme to default theme and test?

Try following code

.front-end-pm-form .fep-button {
    float: right;
}

Try following code

add_filter('fep_get_user_option', function( $value, $option, $default, $userid ){
    global $ultimatemember;
    if( ! $userid )
    $userid  = get_current_user_id();

    if( 'allow_ann' == $option && ! $ultimatemember->user()->is_approved( $userid ) ){
        $value = 0;
    }
    return $value;
}, 10, 4);

Can your website send email? eg. registration, lost password email?
If you send a message, is that notification email sent to your email?
Can you please check and see all fields are filled and give me a screenshot of Front End PM PRO > Settings > Emails? Also please check “From Email” is same domain email of your website and email exists in your server. Some host may block email sending if email not exists.

Please go to Front End PM PRO > Settings > Appearance

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

add_action('wp_loaded', function(){
    if( class_exists( 'Fep_Attachment') )
    remove_action('fep_display_after_message', array( Fep_Attachment::init(), 'display_attachment') );
}, 15 );

Invoice already sent to your email.

Are you trying to send message from “New Message” page or from anywhere else?
Can you type his name in “To” field and his name shows in suggestion?