3.  Whether Macbeth had children or (as seems usually to be supposed) had none, is quite immaterial.  But it is material that, if he had none, he looked forward to having one; for otherwise there would be no point in the following words in his soliloquy about Banquo (III. i. 58 f.): 

                        Then prophet-like
     They hail’d him father to a line of kings: 
     Upon my head they placed a fruitless crown,
     And put a barren sceptre in my gripe,
     Thence to be wrench’d with an unlineal hand,
     No son of mine succeeding.  If’t be so,
     For Banquo’s issue have I filed my mind.

And he is determined that it shall not ‘be so’: 

     Rather than so, come, fate, into the list
     And champion me to the utterance!

Obviously he contemplates a son of his succeeding, if only he can get rid of Banquo and Fleance.  What he fears is that Banquo will kill him; in which case, supposing he has a son, that son will not be allowed to succeed him, and, supposing he has none, he will be unable to beget one.

I hope this is clear; and nothing else matters.  Lady Macbeth’s child (I. vii. 54) may be alive or may be dead.  It may even be, or have been, her child by a former husband; though, if Shakespeare had followed history in making Macbeth marry a widow (as some writers gravely assume) he would probably have told us so.  It may be that Macbeth had many children or that he had none.  We cannot say, and it does not concern the play.  But the interpretation of a statement on which some critics build, ’He has no children,’ has an interest of another kind, and I proceed to consider it.

These words occur at IV. iii. 216.  Malcolm and Macduff are talking at the English Court, and Ross, arriving from Scotland, brings news to Macduff of Macbeth’s revenge on him.  It is necessary to quote a good many lines: 

Ross. Your castle is surprised; your wife and babes
Savagely slaughter’d:  to relate the manner,
Were, on the quarry of these murder’d deer,
To add the death of you.

Mal. Merciful heaven! 
What, man! ne’er pull your hat upon your brows;
Give sorrow words:  the grief that does not speak
Whispers the o’er-fraught heart and bids it break.

Macd. My children too?

Ross. Wife, children, servants, all
That could be found.

Macd. And I must be from thence! 
My wife kill’d too?

Ross. I have said.

Mal. Be comforted: 
Let’s makes us medicines of our great revenge,
To cure this deadly grief.

Macd. He has no children.  All my pretty ones? 
Did you say all?  O hell-kite!  All? 
What, all my pretty chickens and their dam
At one fell swoop?