The trust I'm setting up has a different trustee to the appointor and beneficiary. The trustee lives in Australia but the appointor/beneficiary lives in Italy. Is this ok?
Yes. The reason for this is often because the person with control over the trust is overseas (e.g., Italy), but they want the trust to be resident in Australia, meaning they need an Australian trustee.
The more important thing is that a beneficiary is represented as an appointor (though even this may not be crucial), because the appointor(s) can remove the trustee and appoint a new one if they like. This effectively means the appointor has overall control of the trust at the end of the day.