What is Macduff's birthplace in Shakespeare's Macbeth?

Shakespeare never specifies exactly where Macduff was born, but, since he's identified as the Thane of Fife, we can assume that he was accordingly born in Fife. While the location of his birth is never discussed at length, it's worth noting that Macduff's birth is of vital importance to the plot of Macbeth. The Weird Sisters predict Macbeth cannot be killed by one born of woman, which initially seems to be a pretty solid indication of Macbeth's safety. During his final battle with Macbeth, however, Macduff reveals he was not technically "born of woman," but was actually delivered through a cesarean operation, meaning he was cut out of his mother's womb. Thus, Macduff is not actually "born of woman," meaning he can defeat the tyrannical Macbeth on the battlefield. 

What is Macduff's date of birth in Macbeth?

Unfortunately, Macduff is an entirely fictional character, but your question does point towards the question of where Shakespeare obtained his source material to write the play Macbeth.

Shakespeare used Holinshed's Chronicles which were published in 1587 as his source, in particular focussing on the narratives of King Duncan and King Duff. In this source, Macduff only appears after Macbeth has committed regicide and ruled as King of Scotland for ten years. Macduff shows his opposition against the monarchy of Macbeth by refusing to contribute to Macbeth's building of Dunsinane castle. Macduff, fearing Macbeth, leaves for England to try and encourage Malcolm, Duncan's son, into deposing Macbeth. Meanwhile, Macbeth kills the entire family of Macduff in his absence. As in the play, Macduff, with Malcolm, invades Scotland and kills Macbeth. So you can see that this character is very closely modelled on the original source.

Apart from this literary source, what else we know is that the Clan MacDuff was a very important family in Fife during the medieval ages, both in terms of prestige and power. So sorry - no dates, but I guess with an assignment like yours you can be "creative" in your obituary!