Well, he didn't exactly discover it. He did some calculations about its orbit, and concluded that this particular comet (observed by other people) was the same that had been seen about 76 years...
The first "certain" appearance of Halley's Comet is from 240 BC, in the Chinese chronicle Records of the Grand Historian or Shiji, which describes a comet that appeared "in the east and moved north".
Depends. Halley didn't discover the comet, mearly recognised it as a periodic comet from data recorded by Petrus Apianus in 1531 (German) and Johannes Kepler in 1607 (also German). Halley (English)...