For the United Nations, last week was a week of champagne and euphoria. Even the U.N. fountain, dry for three years of financial drought, was splashing again in the autumn air - a sign of happy times.

There was the Nobel Peace Prize for U.N. peacekeeping and the farewell speech of President Reagan, who finally praised the world body.Reagan and other speakers hailed peace agreements, talks or prospects of peace in Afghanistan, the Iran-Iraq war, Southern Africa and Namibia, Cambodia and the Western Sahara - conflicts in which the United Nations has played or will play a major role resolving.

So popular is the United Nations that Britain and Iran chose it as the forum to announce the resumption of full diplomatic relations.

China and the Soviet Union chose it to announce the first working visit of a Chinese foreign minister to Moscow since the 1950s, a major step toward a Sino-Soviet summit.

At the United Nations, Chinese and Soviet foreign ministers also discussed Cambodia, signaling a new impetus by the communist rivals to solve the problem of Vietnamese occupation.

Soviet Foreign Minister Eduard A. Shevardnadze and Democratic presidential candidate Michael Dukakis chose the General Assembly and the nearby Waldorf Astoria to meet.

Even the fountain in the U.N. Plaza, turned off in a fiscal austerity drive, was turned on in a sign that the United Nations has received both a little more money from the United States and other indebted nations, and a lot more respect.

The high point of the week was Thursday, when the Nobel Peace Prize was awarded to U.N. peacekeeping operations worldwide for 40 years. The Nobel Prize committee cited recent U.N. achievements in mediating an Afghan agreement and in arranging a cease-fire in the Iran-Iraq war.

The three-week General Debate, a parade of world leaders, began Monday when President Reagan addressed the General Assembly of 159 nations and, in a dramatic turnabout, conceded the organization he criticized for seven years was doing a good job.