Hey snypher,
My responses are interleaved below:
what can i do if my SMTP server is outsourced?
This is fine. You go into Admin panel -> emails -> and setup the email. Pay special attention to the section entitled "SMTP Settings (Optional)"
what can i do if i haven't administrative access to the mail server and i can't create a relay rule in this server?
I'm not real sure why you would need to. HAve them setup the account you want as a POP or IMAP account and configure OST with the information you need to poll it. (also in Admin panel -> emails)
what can i do if my SMTP server is remote and request authentication but osTicket don't provide authentication to this?
OSTicket does have a place to configure SMTP Auth. Go to Admin panel -> Emails and set Login information and make sure Authentication Required? is set to enabled.
what can i do if osTicket use php mail function but this one not support authentication?
Ummm... to the best of my knowledge phpmail doesn't support authentication anyway. (I could be wrong about this part)