Is it only when you are logged in as admin? If you are logged in as other role, eg. Editor, can you send message?

Did you get any error? Or nothing happen when you click new message button?
Can you give me access to your website so that i can try?

Please try now, Let me know.
Also change all of your passwords when done.

Please let me know to which user i can send a test message?

Message title is required to send message but you have added display none to message title. Please remove following code

.fep-form-field-message_title{
	display: none !important;
}

Let me know.

You have added content: "\f0dc"; in your .fep-bulk-action::before, .fep-filter::before, .fep-filter-heads-div::before. Please remove it.

Please deactivate autoptimize so that you will get exact file location from where that value is coming.