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.
Ratzinger chose the pontifical name Benedict, which comes from the Latin word meaning "the blessed", in honour of both Pope Benedict XV and Saint Benedict of Nursia. Pope Benedict XV was pope during the First World War, during which time he passionately pursued peace between the warring nations.(...) The Pope explained his choice of name during his first General Audience in St. Peter's Square, on 27 April 2005:
Filled with sentiments of awe and thanksgiving, I wish to speak of why I chose the name Benedict. Firstly, I remember Pope Benedict XV, that courageous prophet of peace, who guided the Church through turbulent times of war. In his footsteps I place my ministry in the service of reconciliation and harmony between peoples. (...)
Now going back to the main subject.
The last Austrian-Hungarian emperor Charles I wanted to sign peace:
In 1917, Charles secretly entered into peace negotiations with France. He employed his brother-in-law, Prince Sixtus of Bourbon-Parma, an officer in the Belgian Army, as intermediary.
He was then beatificated by Catholic Church for his efforts:
Pope John Paul II declared Charles "Blessed" in a beatification ceremony held on 3 October 2004, and stated:
The decisive task of Christians consists in seeking, recognizing and following God's will in all things. The Christian statesman, Charles of Austria, confronted this challenge every day. To his eyes, war appeared as "something appalling". Amid the tumult of the First World War, he strove to promote the peace initiative of my Predecessor, Benedict XV.
The US President, Woodrow Wilson also made some peace attempts before 1917:
He offered to be a mediator, but neither the Allies nor the Central Powers took his requests seriously. Republicans, led by Theodore Roosevelt, strongly criticized Wilson's refusal to build up the U.S. Army in anticipation of the threat of war. Wilson won the support of the peace element (especially women and churches) by arguing that an army buildup would provoke war. (...)
On December 18, 1916, Wilson unsuccessfully offered to mediate peace. As a preliminary, he asked both sides to state their minimum terms necessary for future security. The Central Powers replied that victory was certain, and the Allies required the dismemberment of their enemies' empires. No desire for peace or common ground existed, and the offer lapsed.
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.