Time to write an essay.
So the world has already suffered two wars, both of them having major casualties for both the "winners" and the "losers". I am using quotes on these two words because in war there might be a country or two that win some ground or some natural resources or money, but regardless the casualties and the families destroyed are no much to whatever you won during the war.
The point is, that despite having politicians and personal interests nowadays, contributing to the "decay" of a country, I don't believe that we, as humans and those mentioned above are SO stupid to start a third world war. Because, even in the thought of what casualties this world might have, it's literally a nightmare. Nuclear weapons are one's Plan B in a war, so take into consideration what would happened if every, if not, most of the countries that have nuclear weapons, used them.
Now, regarding what you said about Greece and Turkey, I can assure you that Turkey DOESN'T even want to have a war with us. Why? Because if they do so, they will have a lot to deal with from almost every side, if you get what I mean. Plus, almost every country that has significant power in the EU including also America, they are simply saying this over and over again to Turkey: "don't do something stupid, or else you will go extinct".
With that being said, the answer to your first topic is no, I don't think there would be a third world war.