The D. C. City Council began its fourth legislative session since home rule with a short and proper inaugural ceremony on the front steps of the District Building yesterday, followed by a heated meeting in the council chambers that immediately underscored the fragile power of Council Chairman Arrington Dixon.

The five council incumbents reelected in November, and realtor H. R. Crawford, the newly elected Democrat from Ward 7, were sworn in during a noontime ceremony beneath a windswept red-and-white canopy.

There was less pomp than in past inaugural ceremonies, with the exception of Crawford, the only new member, who arrived in a 20-car motorcade following a mass and a breakfast with about 300 of his Ward 7 supporters at St. Francis Xavier Church on Pennsylvania Avenue in Southeast Washington.

Nevertheless, Mayor Marion Barry said, "the moment is no less historic today than it was in 1975," when the first elected council was sworn in. Barry said that he and the new council would have to press the incoming Reagan administration and the more conservative 97th Congress for complete budget autonomy and a higher federal payment.

D. C. Del. Walter E. Fauntroy said that as the District entered its sixth year of limited home rule, "Thousands in our city are afraid of the future. The cold breath of fear can be felt all around us."

Instead of fear, Fauntroy said, all District residents must have "faith in ourselves and in our ability to govern, faith in the Congress of the United States and the new president to match our determination to govern ourselves."

The measured tone of the short outdoor ceremony quickly gave way to a bitter and emotional debate in the council chambers upstairs, centered on the appointment of a new chairman for the council's committee on Housing and Economic Development. Its past chairman, Willie J. Hardy (D-Ward 7), did not seek reelection.

After about three hours of debate on what is routinely a ceremonial act, formally naming committee chairmen whose selection is usually agreed upon in caucus, the council voted 7 to 5 to make Charlene Drew Jarvis (D-Ward 4) the temporary chairman of the Housing and Economic Development Committee.

In that same vote, however, the members agreed to force Dixon to nomiate committee chairmen based on seniority of council service. That would mean that Dixon is obliged to nominate Betty Ann Kane (D-At-Large) to be permanent committee head before Jarvis' temporary appointment expires in 90 days.

But the council also voted not to meet as a body again during the rest of this month, meaning that the question of who gets the chairmanship will go unsettled at least until February.

Jarvis, who is somewhat of a protege of Dixon, succeeded him as the Ward 4 representative on the council in May 1979, after Dixon was elected council chairman. Kane, who is considered by some a possible challenger to Dixon in the 1982 election for council chairman, has been a council member four months longer than Jarvis.

Dixon said after the meeting that the newly adopted seniority rule is an unnecessary restriction on his powers, and that he intends to nominate Jarvis as permanent head of the committee anyway.

"Jarvis was, by a majority of the City Council, elected to be chairman" of the committee, Dixon said. "I would expect that we would get on with the work of the council now."

Kane, however, said she expects to be nominated for that chairmanship because "right this minute, there is a temporary chairman, but [jarvis' nomination] is not in conformance with the rules we just adopted."

Kane said the whole episode, which leaves the chairmanship of one of the council's most powerful committees up in the air, has been "a very disruptive and very distateful process."

Theoretically, the rules of operation adopted yesterday would only affect the next two years of council action because each new council adopts its own internal rules and organizational guidelines.

But the council, dominated by Democrats since its inception, has operated remarkably free of the seniority and party procedures that are customary in other legislatures. Non-Democrats have held chairmanships while Democrats have not, for example, and the council has never had a functioning majority or minority caucus. Yesterday's action thus set a precedent for more traditional operations.

On that basis, Dixon argued forcefully, but futilely, that the amendment would restrict the power of future council chairmen. Dixon also said that the senority system in the U. S. Congress had traditionally been used in the past to keep moderate and liberal Congressmen out of positions of power. Dixon called seniority "a position we have publicly fought, locally and nationally for years."

But council member John Ray (D-At-Large), who himself is a Democrat without a committee chairmanship, countered, "Four hundred and thirty-five members can get together and they can decide committee assignments in two days. That's because they have seniority, it is a rational system, it is a fair system, it is sound."

The vote to include a seniority system was taken before the vote on Jarvis' nomination. The first vote split, with Jarvis, Jerry A. Moore Jr. (R-At Large), Wilhelmina J. Rolark (D-Ward 8) and William R. Spaulding (D-Ward 5) voting with Dixon. Voting for the seniority system were council members David A. Clarke (D-Ward 1), Hilda Mason (Statehood-At-Large), Nadine P. Winter (D-Ward 6), Poly Shackleton (D-Ward 3), Ray and Kane. John A. Wilson (D-Ward 2) and Crawford voted "present."

The seniority vote was a major blow to Dixon, whose leadership of the council has been seriously undercut since he was defeated on several key pieces of legislation he championed last year.

Six members who voted for the seniority system have, with some exceptions, challenged Dixon on several major issues in the past. When joined by Wilson, those seven members have been able to constitue a majority that Dixon has not been able to control.

The council also voted yesterday to reestablish a committee on education to oversee the city's public schools, including the University of the District of Columbia.

Legally, the operations of and enactment of policy governing the university and the more than 100 elementary, junior high, high school and specialty schools in Washington are under the auspisces of independent boards. The mayor and City Council act only on budgets for the schools.

But by reestablishing a committee effectively abolished less than a year after former council member Julius W. Hobson Sr. died in March 1977, the council hopes to demonstrate concern for education, which has become an increasingly important issue in the city.

The council voted to make Mason, a former school board member who succeeded Hobson on the council, the chairman of the education committee. Her chairmanship, like that of Jarvis, will be temporary, since the council acted yesterday in the form of emergency 90-day legislation. But her permanent appointment is not expected to be as controversial.

Wilson, 36, a former activist with the Student Nonviolent Coordinating Committee (Sncc), and a political consultant, was elected to his third term representing Ward 2, which includes the inner city neighborhoods of Shaw, Dupont Circle, Southwest and Foggy Bottom.

Jarvis, 39, a researcher, was elected to her first full term to represent Ward 4, which includes most of upper Northwest Washington. Moore, 62, the pastor of the Nineteenth Street Baptist Church, was also elected to his third term as an at-large member. He was a member of the appointed City Council, as well.

Rolark, 61, a lawyer, was elected to her second term representing the Anacostia, Washington Highlands and Congress Heights sections of Southeast and Southwest Washington. Ray, 36, a lawyer who was elected in 1979 to fill the seat vacated when Barry was elected mayor, was sworn in yesterday for his first full term.

Crawford, 41-year-old realtor and president of his own real estate management company in Landover, Md., was elected to succeed Hardy as the representative of the area that includes the far northeast-southeast tip of the District.

A former assistant secretary of Housing and Urban Development, Crawford campaigned as a longtime resident of the area. He is strongly opposed to rent control, and he has said that he wants to push for more low- and moderate-income housing, as well as for more small business development, in Southeast Washington.

Crawford was assigned yesterday to serve on the Human Resources and Finance and Revenue committees.