Did any of the great powers reach out to try and resolve the conflict before the Central Powers surrendered in 1918? Not counting the treaty of Brest-Litovsk, of course, because that didn't end the war as a whole.
Just to mention, as he was not from "great powers", the Pope Benedict XV made several attempts to make both sides sign peace.
Now going back to the main subject.
The last Austrian-Hungarian emperor Charles I wanted to sign peace:
He was then beatificated by Catholic Church for his efforts:
The US President, Woodrow Wilson also made some peace attempts before 1917:
Yes there were. There were many both public and private, some by quasi non governmental organisations, countries still outside the conflict and concerned citizens. I can recommend http://archive.org/ as a source of material on this subject especially the Carnegie Endowment for International Peace which has a number of original documents on this subject. "Official communications and speeches relating to peace proposals" from Brigham Young University illuminates but does not enlighten.
A peace treaty would have been very difficult in 1914, impossibly hard in 1915 and unreachable thereafter. All the warring parties had lost too much, had unreachable goals of winning and were stuck in a mental morass of their own choosing.
An interesting published set of proposals from the German Social Democrats is worth mentioning. In exchange for peace, the British would disarm their fleet, accept German garrisons in the channel ports, allow Belgium to be neutral with German oversight and the French to pay for it all. This is, of course , from the socialist side of German life who , whilst initially opposed the war, voted tax credits to pay for it and marched off to war.
None of the proposals, President Wilson's was the best shot on this although 'Freedom of the Seas' is such a relative term.
 Churchill . A history of the English speaking peoples.