Why didn’t Turkey claim any Greeks island near their shores?

They did: Imbros and Tenedos. Like the other islands, they were substantially ethnic Greek, but they remained in Turkey under the Treaty of Lausanne, presumably because of their strategic importance outside the Dardanelles.

Of the other Aegean islands near the shores of Turkey, the islands from Samos up were ceded to Greece by the Ottoman Empire in the aftermath of the First Balkan War; the Dodecanese went to Italy instead, and were integrated into Greece in 1946.

Fine print in the treaty around the Dodecanese led to the Imia/Kardak sovereignty crisis in 1996. The West Wing made fun of the incident a few years later, situating it on the Greek/Albanian border. I was in Greece at the time, and it was not effing funny.

As for claiming, well, Turkey lost the Balkan War, hence losing most of the islands, and won the Turkish War of Independence, thus getting to claim two strategic islands. Right and wrong doesn’t enter into it, and nor does self-determination; but FWIW, the population of the islands was substantially ethnic Greek even before the population exchanges—although a Turkish minority has remained in place in the Dodecanese, which were not subject to the exchanges.

Should I speak with an Australian accent when I go to Melbourne for uni?

Adrian Beale has the right answer. We’re quite used to people with different accents. The divide is more about international students not having the confidence to associate with the locals, which becomes a self-fulfilling prophecy. Reach out to locals, and they will befriend you; no need for the accent. We do judge, but we judge on demeanour, not on accent.

In my day (early 90s), the International Students numbers were lower—which meant that it was more difficult for international students to segregate. My main social group during Engineering, as it turns out, was East Asian. The group included people with Ocker accents (from the country), people with the East Asian variant of Received Pronunciation, and people with more clearly Chinese accents. In retrospect, I realise that I did not have a clear idea who was just off the boat, who studied here in high school, and who was descended from Chinese who came to the goldfields in the 1850s. (My money was on the Ocker sounding guy.)

It was clear that the group was mainly East Asian, plus one Greek (me) and one Fijian Indian. It was also clear that I wasn’t unwelcome, and that the group was not particularly insular. There was a countergroup of Anglos, who didn’t associate socially with the East Asian group, but certainly didn’t shun them either.