Shamim's Plugins

assuming your php version 5.3+
Add following code in your theme’s functions.php (child theme’s if any)

add_filter( 'fep_eb_email_legends', function( $legends, $post ){
	$legends[ 'sender_username' ] = array(
				'description' => __('Sender Username', 'front-end-pm'),
				'where' => array( 'newmessage', 'reply' ),
				'replace_with' => ! empty( $post->post_author ) ? fep_get_userdata( $post->post_author, 'user_login', 'id' ) : ''
				);
	return $legends;
	
}, 10, 2);

Then go to Dashboard > Front End PM > Settings > Emails. use {{sender_username}} to send username in emails.

your theme should allow admin-ajax.php. There should be any option or any other way to allow this call.
Please contact your theme author.

My phone also have 4.0.4, so that is not an issue.
Please check your phone if there is enough memory or network problem or any other problem.

in my test website i have sent 1 pdf file and 1 png file and download from android phone. Everything working perfectly.

Can you please make a test user in your website and send some attachments. Then give access to me So that i can try.

When non admin user try to access your website admin area they see a error that they do not have permission to access. Which plugin show that error message?

your admin-ajax.php is blocked for non admin users by any other plugin or custom code. So non admin users can not create ajax request from front end.
You should consider unblock admin-ajax.php

according to current version (4.8), only first message of the thread will count. when you send a message that will be in “Sent” filter and when someone will sent you a message that one will be in “Inbox” filter. Any reply message does not change message position to another filter.

Not file permission, Some website block admin access for users.
Please give me credentials here, check “Set as private reply”