Artificial heart recipient William J. Schroeder has sold the exclusive rights to his life story to Life magazine, the magazine said yesterday. Terms of the agreement weren't announced, but the magazine's science editor, Jeff Wheelwright, said the story would be the cover story of the May edition . . .

President Reagan plans to nominate Martha Graham, founder and director of the Martha Graham Dance Company in New York, as a member of the National Council on the Arts. . .

Actress Vanessa Redgrave plans to appeal a recent court ruling that upheld the Boston Symphony Orchestra's right to cancel an appearance by her as a result of political considerations. At a news conference Thursday, she also said she will miss Monday night's Academy Awards for the funeral of her father, Sir Michael Redgrave, who died this week. She has been nominated for a best-actress Oscar for "The Bostonians" . . .

The estate of the late playwright Tennessee Williams has filed a $2 million suit against Bill Barnes, Williams' former agent, seeking custody of a set of journals Williams kept in the 1930s and 1940s. Lawyers for the Southeast Bank of Miami, which represents Williams' estate, have asked for a restraining order preventing the agent from selling the journals until after a hearing . . .

Surrealist painter Salvador Dali, 80, was taken to a hospital last night in Catalonia in northeast Spain. A nurse at his home said he entered for an "ordinary medical" . . .

Actor Richard Burton left some $2.7 million in his will, most of it to his fourth wife, Sally, according to a copy of the will released in Hamilton, Bermuda, yesterday. Burton, who died at his Swiss home last August, also bequeathed sums to his children, to those of Elizabeth Taylor, whom he married twice, and to the schoolteacher who encouraged him to become an actor . . .