In the play Macbeth, who kills Macduff's wife and child?
Yes, Macbeth certainly did hire murderers to kill Macduff's wife and children. Let's look at the text before we explore your further questions:
The castle of Macduff I will surprise; / Seize upon Fife; give to th' edge o' th' sword / His wife, his babes, and all unfortunate souls / That trace him in his line. No boasting like a fool; / This deed I'll do before this purpose cool. (4.1.150-155)
There is no denying Macbeth's words here. He is the culprit. Period. The details of his plans, however, are in the next lines:
But no more sights!--Where are these gentlemen? / Come, bring me where they are. (4.1.155-156)
Here is the first inkling that Macbeth intends to hire murderers to do this job. Not just one "murderer," but "murderers" in that he says "Where are these gentlemen?" That means more than one, of course.
This is reiterated in the stage directions from Act 4, Scene 2 where it says "[Enter MURDERERS]." There we are again, "MURDERERS" clearly means more than one. I suppose it is up to the director exactly how many murderers he/she would like to use. These murderers subsequently kill Macduff's whole family.
In fact, according to eNotes, Macbeth's first encounter with the murderers involves exactly THREE murderers in his attempt to kill Banquo and family. "He plans to meet the murderers again. These may be the murderers who kill Lady Macduff also." Therefore, it's possible that there are exactly three murderers involved in the Macduff incident.
Therefore, the answer to your secondary question is, "Yes, Macbeth hired men to kill Macduff's family." How many? "More than one, possibly three."
In Shakespeare's Macbeth, it is Macbeth that orders the death of Macduff's wife and children after he finds out that Macduff has left England. Macbeth does this because he is uncertain of his own position in the kingdom. After ordering the death of Banquo and Fleance, Banquo's ghost is the one that spooks him. Macbeth then goes to the three witches and they tell him that Macduff is the one he should fear.