The last remaining Iranian diplomat departed from Washington last night, leaving behind a series of unanswered questions, a flock of FBI agents, weary State Department officials and a foiled plot for a best-selling spy novel.

Who was Abdol Azim Biabani and why was he suddenly taken to a suburban Maryland hospital Tuesday afternoon, hours before he and his family were scheduled to depart as President Carter had ordered?

The first report said the finance minister and second in command at the Iranian embassy had suffered a heart attack. Another story said he had asked for political asylum. A third report stated he had been fired or had quit his post several days ago. Or was he a double agent, ready to defect?

The mystery surrounding Biabani, who rested in the coronary care unit of Suburban Hospital guarded by three burly FBI agents, kept State Department officials denying rumors while reporters staked out the family's brick home in Bethesda.

Finally, at 5:30 p.m. Biabani was taken from the hospital to his home. Then he and his family were ushered off to Dulles Airport in a yellow Impala.

"My mind, I can't concentrate," said Biabani's wife from behind their front door while several dozen neighbors and friends stood outside, waiting to wave goodbye.

"I can't eat, I can't talk. I just sit here and look after my children. I don't know yet when we have to go. How can I leave my husband in this situation. And there's all the equipment [furniture] in the house."

Biabani, described as a gentle, pleassant career diplomat of 45, came to the United States four years ago. His tour of duty was to end in June. Although he told associates he was looking forward to returning home, freinds and neighbors said yesterday Biabani had no intention of going back to Iran. According to one neighbor, Biabani said that, because he had worked at the embassy under the Shah's regime, he was afraid he would be killed in Iran. Instead, the neighbor said, Biabani planned to live in London where a relative now resides.

Thomas Shack, one of several lawyers for the former Iranian embassy, said yesterday that report would be "inconsistent" with his personal experience. "It was my understanding that he was going back to Iran," said Shack. "In fact, he said he was looking forward to it."

Was Biabani's sudden heart ailment a ruse, designed to win him time to seek political asylum? State Department officials refused to comment, except to say that no one had been granted asylum.

One official said every Iranian diplomat had asked to stay in America for one reason or another ("One said he had bought a new car, another said his wife didn't want to leave. They all claimed it would be bad to take children out of school." But no one could say for sure what condition Biabani was in or whether he had suffered a heart attack.

"He's a heavy smoker and overweight," offered Michael Maggio, another lawyer for the Iranian embassy. "A classic candidate for a heart attack. I find it believable."

As the family's suitcases were being packed into cars yesterday, 17-year-old Jeff Lerner sat on his bicycle in the Biabanis' driveway." I used to play soccer, baseball and kickball with them," the teen-ager sighed. "I'm sorrt to see them go."

The Biabanis have two sons, Arash, 14, and Borzoo, 11.

Lee Shefferman, 10, said he had visited the family Tuesday night. "I asked Borzoo if he really wanted to go and what he thought of Jimmy Carter," Shefferman recalled. "He said he doesn't want to leave and he hates Carter's guts."

Another family friend said the Iranian diplomat's 11-year-old son had given his girlfriend a gold chain with two hearts on it as a goodbye gift. "His girlfriend was really sad that he had to go."