Yes, there was a real Macbeth, (Mac Bethad mac Findláich), who lived from 1005 to 1057(ish--accounts vary). The original Macbeth did kill Duncan, but he did so in battle. Also, unlike Shakespeare's Macbeth, the real Macbeth ruled for 14-17 years, and by all accounts he was a good king, creating order and protecting women and children. According to the BBC site, he ruled until he was overthrown by Malcolm, who killed him in battle. Others say his son succeeded him, but only for a year, when he was killed by Malcolm.
Yes, there was an actual man namede Macbeth.
In history, he was born around 1005. In August 1040, he killed Duncan I, in battle so he became king. His marriage to Kenneth III's granddaughter Gruoch strengthened his position.
Macbeth ruled fairly, imposing law and encouraging Christianity. He was a courageous leader and made successful trips over the border