Billy Carter, whose correspondence with the Justice Department over Libya began eight months ago, wrote in August, asking for the forms necessary to declare himself a legally registered foreign agent. The request came, a source says, just as he was preparing to leave for Tripoli to celebrate the 10th anniversary of the Libyan Revolution. By the strictest interpretation of the law, he has 10 days after his return to file his declaration if he decides to become Col. Qaddafi's representative. . . .

. . . When the students took over the Libyan Embassy here recently, a lot of hearts were broken all over town. Chard d'Affaires Ahmed Madfai, who looks like Gregory Peck made up to look like Rudolph Valentino, was a man who was forever getting bouquets of flowers with little notes -- presumably from women who didn't know he is married and the father of a score of children. In Libya last week, he will be returning, one source says, to take over "procurement" for the embassy. Procurement of raw materials and manufactured goods.

. . . Former secretary of state Henry Kissinger will "make a major foreign policy speech to be covered by the networks" when he appears at a fundraiser for John Connally in Fairfield, Conn., Sept. 29, according to those staging the event. Kissinger, who sometimes gets paid as much as $1,000 per minute for his crowd-drawing appearances, isn't billing the Connally people anything. Security, at the request of Kissinger's staff, will be "supertight" this time. . . .

. . . Sources familiar with the facts and figures -- which are partially classified because of the security methods involved -- say that Secret Service protection for ex-president Gerald Ford passed $1.2 million last year -- the highest ever for any former chief executive. "It's the traveling," says one source. "He's in a different city ever day, sometimes day after day after day. And it's not just his bodyguards who go along. A military bomb squad and all kinds of other people are kept in transit" . . . Ford's wife, Betty, isn't keeping up with his grinding itinerary at the moment. But she has the new wardrobe for campaigning if she wants to go along. Daughter Susan, eyeing all the new outfits hung around her mother's bedroom in Palm Springs recently, voiced her envy.

"Get a job, darling, get a job," advised her mother. That's why she went back to her career in professional photography. . .A Washington professional woman who dated presidential assistant Hugh A. Carter Jr. says she can't understand why everyone calls him "Cousin Cheap." Once when she felt faint at a party, he offered to summon a White House helicopter to whisk her home . . . In a current Ladies Home Journal article titled "How love and religion are changing Ol' Blue Eyes," reference is made to the fact that Houston heart surgeion Dr. Michael De Bakey is an old friend who is a frequent house guest at Frank Sinatra's Palm Springs compound. What isn't mentioned is that he met the current Mrs. De Bakey there on one of those visits. . .Sen. Gary Hart's office, in confirming that the Colorado Democrat and his wife, Lee, are "living separately," wants to stress that the arrangement is "for the time being because of certain stresses." Lee Hart now has a lucrative career of her own. The magazine "Real Estate Washington" recently listed her among the 14 congressional wives now selling real estate here. Together, the article estimated, the women had sales of more than $15.5 million last year. . .In the middle of Hurricane David's devastation in Washington, Tongsun Park arrived back in town. His old chauffeur was waiting at Union Station to whisk him out of the wetness into a waiting limousine. Before he left Seoul, he gave a party for the stars of the movie "Inchon." Actor David Janssen says he didn't know who his host was (since Park is as common as Smith in Korea) until he drove through the gates of Yongsun's villa and saw the burly bodyguards. "Then I realized it was THAT Mr. Park," he says. "The only gift he gave me was a cake of ginseng soap. I broke it open, hoping to find a diamond, but there wasn't even a fortune cookie message". . .Chip Carter, who has become the unofficial booking agent for all movie shows at the White House and Camp David, has been asking only for comedies recently.