Eurovision is organised by the European Broadcasting Union, which includes basically all countries in the European Broadcasting Area (basically Europe + all of the Mediterranean). Those include Morocco, Tunisia, Egypt, Israel, Armenia, etc. They have always been allowed to participate. Australia is an outlier. They just got a special invitation.
Theoretically yes, but associated members (in contrast to full members) still need to be approved on a case by case basis.
https://en.wikipedia.org/wiki/Eurovision_Song_Contest#Participation