There's a conspiracy theory right there! No-one really knows how Shakespeare died, but, as there's nothing in the civil and legal documents telling us it was a murder, it seems unlikely that he was killed. He probably just died of old age.
Some scholars think that the signatures on his will, which he signed on March, 25, 1616, tell us he was sick. That seems a little bit of a stretch to me, though it's not been entirely discredited by scholars. John Ward - a Stratford vicar - wrote in his diary some fifty years after Shakespeare's death that "Shakspear Drayton and Ben Jhonson had a merry meeting and it seems drank too hard for Shakespear died of a feavour there contracted." This is just a rumour though - and written after, long after, the event.
But most likely is that he just died of old age.
Shakespeare was buried on April 25, 1616 in Holy Trinity Church, in Stratford (you can visit his grave, even today!) which is where had been baptised some 52 years earlier. Shakespeare was baptised on April 26th 1564, and entered into the register. It was common to baptise children three days after birth, so it seems likely that Shakespeare was born on April 23rd. And that is also the date he died.
Hope it helps!
As far as I know, He died out of sickness and age. He wasn't muedered. Maybe you are beeing confused with Christopher Marlowe.
And yes, He died on his Birthday.
It is unlikely that Shakespeare was killed, but no body really knows. He was most likely sick, as the plague still frequented Europe until about the 1700s (almost 100 years after his death). It is commonly thought that Shakespeare's death date is the 23rd of April, but it is unknown whether his birthday was the 23rd of April.