Wikipedia has a partial answer to my question re Australian participation in Eurovision:

"Participation in the contest is primarily open to all broadcasters with active membership of the European Broadcasting Union (EBU). To become an active member of the EBU, a broadcaster has to be from a country which is covered by the European Broadcasting Area or a member state of the Council of Europe.[1] Eligibility to participate is not determined by geographic inclusion within the continent of Europe, despite the "Euro" in "Eurovision", nor does it have a direct connection with the European Union. Several countries geographically outside the boundaries of Europe have competed: Israel, Cyprus, and Armenia, in Western Asia, since 1973, 1981 and 2006 respectively; Morocco, in North Africa, in the 1980 competition alone; and Australia making a debut in the 2015 contest."

footnote 1. https://www.ebu.ch/about/members/admission
"Admission". EBU. European Broadcasting Union. Retrieved 12 April 2017.
https://en.wikipedia.org/wiki/List_of_countries_in_the_Eurovision_Song_Contest also gives a list, with some details, of countries which have unsuccessfully applied to join the competition