Hans-Dietrich Genscher, West Germany's foreign minister and the target of criticism for his role in the creation of the new Bonn government, was elected tonight to his 10th term as chairman of the pivotal Free Democratic Party by a margin of 222 votes to 181.

By a narrower margin, delegates to the party's national convention also formally endorsed the Free Democrats' new alliance with conservative Chancellor Helmut Kohl.

Both results were reassuring for Kohl, who needs the small centrist party to balance the right-wing Bavarian faction of his Christian Democrats in the Bonn government.

But, still in turmoil over their break two months ago with former chancellor Helmut Schmidt, the Free Democrats passed a sharply worded resolution disapproving of the way the coalition change was managed by Genscher. The resolution complained of a "lack of information and participation" afforded the party's rank and file.

Also unhappy with the weight that they have been given in the new government, the Free Democrats served notice on Kohl that the coalition agreements that have been negotiated are "insufficient."

An additional threat to the stability of the new Bonn partnership comes in left-wing challenges, scheduled for voting on the convention floor Saturday, to the Free Democrats' previous support of the North American Treaty Organization's plans to deploy additional nuclear missiles in Europe.

Several resolutions to be offered urge either withdrawing support for NATO proposals to station Pershing II and cruise missiles in Western Europe beginning late next year or setting new conditions for such deployment, including withholding party approval until a special party congress in 1983 to review the progress of U.S.-Soviet arms reduction talks.

This reflects growing opposition to nuclear weapons among West Germany's liberals, similar to the views that eroded Schmidt's authority in his Social Democratic Party and encouraged Genscher to abandon the former coalition with Schmidt. In the same way, agitation in the Free Democratic Party against the missiles could undercut Genscher's relationship with Kohl.

Genscher devoted his opening address to a plea to hold to the NATO decision, and he sought to assure party members that the United States and Moscow are negotiating seriously and the Geneva talks on reducing European-based nuclear weapons have "rushed forward" to matters of substance.

At the same time, Genscher said that he does not expect "substantial progress" in the negotiations until the summer of 1983 at the earliest. He stressed that a breakthrough would come only if the Soviets were convinced of the West's resolve to follow through on its plans for the new missiles.

"Nothing should obscure the simple realization," Genscher said, "that we are not threatened by Western medium-range missiles that do not exist, but we are threatened by Soviet SS20 missiles that already are aimed at us."

Genscher's estimation of progress by next summer was more optimistic than a recent public statement by U.S. disarmament chief Eugene Rostow, who predicted no movement in the talks until "five minutes before midnight." The prospect of a prolonged impasse in the Geneva negotiations puts greater pressure on the Bonn government to maintain lagging national support for NATO's negotiate-and-deploy approach.

In language reminiscent of Schmidt's admonition last year to some Social Democrats to remember which side they are on, Genscher used the location of his party's convention in the divided city of Berlin to drive home a NATO alliance lesson.

"Here in Berlin, it is clear how incorrect are those who would have us believe that we must keep an equal distance between the United States and the Soviet Union," he said. "Here, one knows that American troops stand by us so that free trade unions can exist, and Soviet troops stand in Poland so that, there, no free trade unions can exist."

Although skillful in the past at bridging his party's left and right wings, Genscher's awkward handling of the change in the Bonn coalition clearly has eroded his authority. Deep divisions were evident in today's embittered debates on the future course of the Free Democrats