Questions 1 and 3 are based on this passage

The recently announced discovery of the first known planet orbiting a pulsar (the ultradense, pulsating remnant off the supernova explosion of a star) turned out to be based on faulty data. Had this discovery been confirmed, theorists would have had difficulty accounting for the existence of such a planet. The supernova would certainly have destroyed any preexisting planets. This particular pulsar is relatively young, allowing little time for a new planet to have coalesced, and it rotates relatively slowly, implying that it has not interacted with any nearby star since the supernova. But newer evidence of a different pulsar with planets is more promising. This is a rapidly spurring “millisecond pulsar” thought to be a much older object that has pulled gaseous material from a stellar neighbor, causing its rotational speed to increase. Leftover, unconsumed gas around such a pulsar could, in theory, coalesce into planets. Or the pulsar’s radiation might have vaporized a companion star, providing new material for planetary formation.