input name attribute value name is reserved by WordPress, this is the problem i have found after visiting and testing your form, simply replace name=”name” with name=”fullName” etc.
<input type="text" name="name" placeholder="Name*" value="<?php echo esc_attr($_POST['name']); ?>" />
to
<input type="text" name="fullName" placeholder="Name*" value="<?php echo esc_attr($_POST['fullName']); ?>" />