1. This has no bearing on claiming the motgage interest as an expense.
2. The only interest allowable is that incurred in purchasing that specific property. If you have a mortgage of say €300,000 on the property, of which €50,000 relates to the original amount outstanding on the house and the rest relates to your house in Australia, then you can only claim for the interest on the €50,000.
Also, you need to appoint a person here in Ireland as a collection agent for your rental income. They are assessed as 'Joe Bloggs as Collection Agent for Bovis' and are responsible for making the annual return and paying the tax due on your behalf. This doesn't need to be an accountant/professional, it can be a friend or family member willing to undertake the responsibility.