There are no longer limits on support tickets, so you have unlimited available for all of your products.
It doesn't really matter which goes first, as long as the first one does not specify a redirect page.... so the order you have should work since the update is before the email and has a blank redirect setting.
It really appears this page should work. What is the result you are having? The email gets sent but the password is not updated?
Is it updated in the email and not in the database? or is it updated in the database and not in the email?