What was going on when I was born?

Four United States marines were wounded tonight as shells, mortar rounds and small arms fire struck the Marine compound at the airport here. Two American warships and a Marine shore battery fired back. The action came after heavy fighting broke out between the Lebanese Army and anti-Government forces in nearby southern suburbs of Beirut populated predominantly by Moslem Shiites. For a time, the Beirut radio reported, shells fell at the rate of one every five seconds into the airport area where the marines are based. But a Marine Corps spokesman said later that although heavy fighting continued nearby, the shelling of the airport area had tapered off.

Howard H. Baker Jr., the Senate majority leader, gave Secretary of the Interior James G. Watt a grim assessment today of his standing on Capitol Hill amid mounting demands for Mr. Watt's resignation. Mr. Baker, a Tennessee Republican, told Mr. Watt that his effectiveness as Secretary had been seriously impaired by his remark Wednesday that a panel to review his coal-leasing policies was ideally balanced because it included ''a black, a woman, two Jews and a cripple.'' Watt Apologizes to Panelists Also today, Mr. Watt personally apologized to each of the commission members. On Thursday he asked President Reagan to forgive the ''morally offensive'' remark, noting that it came in a speech in which he praised the high qualifications of the panel members. He had followed the offensive remark with the statement, ''And we have talent.''

Adminstration officials said today that President Reagan will make public at the United Nations Monday a new proposal for breaking the deadlock in the medium-range nuclear missile talks with the Soviet Union. The central idea is a higher proposed ceiling on missile warheads for each side worldwide, combined with an agreement by Washington not to deploy all of its permitted missile warheads abroad. The proposed ceiling would allow Moscow to keep a greater number of its more than 1,500 existing missile warheads than the Administration's current position of 300 warheads for each side, and it would thus go far beyond Mr. Reagan's original proposal of zero for each. No Specific Ceiling Administration officials said the new total could run as high as 625 warheads, but that Mr. Reagan had not approved any specific ceiling in the hope of being able to negotiate a lower one.

More than a thousand Government troops beat back crowds of young demonstrators tonight as they tried to advance on the presidential palace. Several shots were fired, and one civilian reportedly suffered an arm wound. Two other demonstrations took place earlier in the day - one by office workers in the financial district and the other by students near the United States Embassy. Both were broken up by tear gas.

A man described by Federal officials as a Bulgarian intelligence agent was arrested on an espionage charge last night as he left a restaurant in Manhattan. He was said to have been carrying highly classified nuclear secrets received from an American who was cooperating with the authorities. The Federal Bureau of Investigation said the suspect, Penyu B. Kostadinov, 41 years old, an assistant counselor for the Bulgarian Commercial Office at 121 East 62d Street, was taken into custody at 7:15 P.M. as he left the Gulf & Western Building on Columbus Circle. Mr. Kostadinov, who lives at 315 East 86th Street and has worked in New York as a Bulgarian trade representative since 1979, was said to have obtained the secret documents from the American at a dinner meeting at the Top of the Park, a restaurant atop the tower on the southwest corner of Central Park.

An order of cloistered Carmelite nuns living here under 13th-century tenets have mounted a rare and so far successful public protest in recent days against a bit of 20th-century suburbia - a proposed five-story glass office building. Amid the nuns' complaints that such a building next to the grounds of their monastery would intrude on their reclusive life of prayer, solitude and avoidance of outsiders, a developer today formally asked the town's Board of Adjustment to put off any action on his application for zoning variances needed for the building. A governing doctrine of the Carmelites, dating from the order's formation in the early 1200's, is that the nuns cannot be seen by outsiders. They fear that a five-story office building would allow people on upper stories to look into the gardens and interior grounds of their walled, 11-acre site and disrupt their dedication to contemplation and prayer.

Argentina's military Government approved a law today granting the military and the police immunity from prosecution for crimes committed during the so-called dirty war against leftists. More than 6,000 people were reported to have disappeared while in the custody of security forces in the antiterrorist campaign. Hundreds more were killed and thousands tortured. The law, which takes effect immediately, also gives immunity to people suspected of terrorist activity, but not to those already convicted or in exile.

Governor Cuomo issued an executive order yesterday designed to make all state agencies buy American-made steel for construction projects. The Governor, whose order sets a cost standard for steel, said he was complying with a ''Buy American'' measure passed by the State Legislature earlier this year. He acted shortly after the Metropolitan Transportation Authority rebuffed his attempt to impose a more flexible cost standard than the one it adopted yesterday for the purchase of American steel for transit projects. Mr. Cuomo denounced the authority as a ''fiefdom'' and reiterated his call for its abolition.

The newly independent Caribbean state of St. Kitts-Nevis was admitted to the United Nations today as its 158th member.

The Acapulco of September is not the one of American tourist fantasies. The people darting in and out of the restaurants and boutiques are not the fashionable or famous, but solid, hard-working, middle- and upper-middle-class Mexicans, looking for a break from the pressures and pollution of city life. The polyglot of English and French and Italian on the beaches is replaced by almost pure Spanish. The hotel staffs seem relaxed with people who understand better their language, their manners, their culture and their situation. Despite Mexico's economic crisis, the middle class appears to have been able to find the money to continue to come here - in droves. Hotel prices, which are under strict Government control, are about the only thing that have not been subject to the country's extraordinary inflation, making vacations, for those in a position to afford them at all, a relative bargain - particularly since the devaluation of the peso has put foreign travel way out of reach for most. ''People change to lesser hotels, or drive instead of fly,'' said a Mexican who has visited here often, ''but they still come.''

Six Democratic Presidential candidates, calling apartheid a ''unique and unconscionable system of legalized discrimination,'' endorsed legislation today that would place stringent economic limits on American relations with South Africa. In a letter to members of the House of Representatives, the six announced their support for legislation that would bar new bank loans to the South African Government, require American companies with more than 20 employees in South Africa to follow fair employment practices, and ban the importation of kruggerand and other South African gold coins into the United States. Last year the sale of such coins in this country amounted to $363 million.

A Gulf Air jetliner crashed and burned in the mountains of this desert sheikdom today and airline officials said all 112 people aboard were killed. The passengers inluded an American. The Boeing 737, on its way from Karachi, Pakistan, to Dubai by way of Qatar on the Persian Gulf, lost contact with the Dubai airport 20 minutes before it was to have landed, airport sources said.