The contact form is displayed inside a modal window and displayed on the page via ajax.
The php function that actualy contains the contact form is function wpestate_ajax_show_contact_owner_form() in ajax_functions.php at line 962 . If you want to add or change anything this is the place where you work with the html code.
The send message action is triggered when you press the send button. This action is also ajax made and the js event is on property.js at line 250
the php function is wpestate_mess_front_end in ajax_functions_booking.php at line 1322