February 5, 1986

President Reagan appealed tonight to Republicans and Democrats to unite in an effort to control Government spending, saying, ''It's time we reduced the Federal budget and left the family budget alone.'' In his annual State of the Union Message to Congress, Mr. Reagan singled out support of the American family as a major theme of the remainder of his second term. He cited the family as the ''moral core'' of a restoration of the nation's confidence in the future. ''Tonight, we look out on a rising America - firm of heart, united in spirit, powerful in pride and patriotism,'' Mr. Reagan said in a nationally televised speech before a joint session of Congress. ''America is on the move!'' Welfare Study Proposed Although the speech contained few details, Mr. Reagan proposed a study of the nation's welfare system and what he termed the ''web of dependency'' among recipients; ordered a Government review of the possibility of providing insurance for the elderly against ''catastrophic illness,'' and directed the Treasury Secretary, James A. Baker 3d, to determine if the nations of the world should meet to discuss the alignment of their currencies to thwart ''wild currency swings.''

International Oil prices dropped further as OPEC indicated it would not limit production. In hectic trading, crude oil prices neared the $15-a-barrel level. They were nearly twice as high as recently as November. An OPEC committee ended its meeting, saying the organization's ''fair share of the world market'' should be higher than its official quota, but OPEC is already exceeding the quota. [ Page A1. ] While contract prices for crude oils plunged, prices of petroleum products finished under 50 cents a gallon. [ D5. ] The Economy The sale of Conrail to Norfolk Southern passed the Senate. The legislation now goes to the House, where it has run into opposition and its prospects are uncertain. [ D1. ]

A year after President Reagan celebrated Clara Hale as an ''American heroine'' in his State of the Union Message, the 80-year-old founder of Hale House has been promised state financing for a new Harlem project that will provide temporary apartments for recovering drug addicts and their children. Mrs. Hale already helps infants through withdrawal from heroin and cocaine in a brownstone at 154 West 122d Street, where yesterday she dandled two babies on her knee while her daughter, Dr. Lorraine Hale, announced the state decision to pay the operating costs of Hale House Center. Apartments and Support The center will occupy a now vacant 31-unit building at Manhattan Avenue and 113th Street, one of 24 city-owned properties that last fall were turned over to nonprofit organizations offering innovative plans to house the homeless. The building is expected to include both apartments and support services for families that were divided when adults entered drug rehabilitation and children were placed in foster care.

A Bonn dispatch on Jan. 28 about Prime Minister Shimon Peres's trip to the site of the Bergen-Belsen death camp referred incorrectly to the year that Prime Minister Yitzhak Rabin visited West Germany. It was 1975.

NEW YORKERS who stack dirty pots and pans in the living room when preparing a meal in their closet-size kitchens probably dream of cooking in a restaurant where, surely, there is a place for everything and everything is in its place. What else besides yards of counter space, breezy passageways and elbow room that accommodates considerably more than a few elbows could be the source of the hundreds of meals produced each day in a top city restaurant? What else, indeed. Meal-for-meal, Manhattan restaurant kitchens have far fewer square feet per person than most apartment kitchens. There are exceptions. The new restaurant Le Bernardin, which opened last week at 155 West 51st Street, has a 2,200-square-foot kitchen, about two-thirds the size of its dining room. Word of this spacious, state-of-the-art cooking space has spread via the restaurant grapevine, and chefs from all over the city have come to peer, poke and marvel. There are no other kitchens like it in New York City and few others like it in the world. It is the dream.