I've heard many times that during the Greco-Turkish war, king Constantine of Greece had thoughts about annexing Constantinople and crowning himself Emperor there, was this true?
I've also heard there was a saying, going like "Constantine built the city, Constantine lost the city and Constantine will reclaim the city", regaridng Constantinople, was it a widespread saying?
The saying is fairly common in contemporary Greece. An equivalent motto is: “Greece has always had one foot in Athens, the other in Constantinople; she’s on one foot now, but soon will tire and put the other one down again”. You find these or equivalent mottos on bumper stickers (the usual interpretation being that the owner holds fairly far-right nationalist views). Not the norm, but not rare either.
The slogans hark back to a nationalist/expansionist Greek movement dating to the founding of the modern Greek state and especially the territorial expansion in the late 19th and early 20th centuries (The Big Idea, Μεγάλη Ιδέα). This made claims for Greek territorial rights based on Ancient Greek city state locations (Magna Grecia), language area, and the successorship to the Byzantine Empire.
You can also find this at the root of why Greeks call Albania “the northern landmass” (Boria Ipiros, Βόρεια Ήπειρος) - the Greek part of that peninsula being called Ipiros (Ήπειρος).
Reading:
Ionian Vision, Michael Llewelyn-Smith. Greek occupation of Ionia in the context of the Megali Idea.
Ataturk, Lloyd George and the Megali Idea: Cause and Consequence of the Greek Plan to Seize Constantinople from the Allies, June-August 1922. Michael Finefrock
Most sources covering the origin of Megali Idea in the mid-late 19C are in Greek, especially the more popular history ones. I am not sure that any have been translated but can have a look.