Macduff's conflicts are primarily external.  He leaves his family and goes to England in hopes of convincing Malcolm to return to Scotland and take back the Scottish throne by force. Clearly Macduff's conflict is with Macbeth.  Macduff views Macbeth as the enemy who is destroying his country.  He describes the damage Macbeth has done to Scotland:

Each new morn

New widows howl, new orphans cry, new sorrows

Strike heaven on the face . . .

Later, Macduff learns that his wife, children and servants have all been killed by Macbeth.  Again, his conflict is external.  Macbeth vows to fight Macbeth "front to front." Since Macduff has no soliloquies, it is difficult to determine whether or not he has internal conflicts.  However, it might be assumed that he may have struggled with leaving the family he clearly loves and going to Scotland.  In other words, when he had to choose between his country and his family, he chose his country.  When he finds out that his family is dead, he blames himself:

Sinful Macduff,

They were all struck for thee! Naught that I am.

Not for heir own demerits but for mine

Fell slaughter on their souls.

Macduff feels responsible for their deaths, and struggles in this scene between his guilt over leaving them, his extreme grief, and his need to revenge.  In fact, his emotions quite overcome him as he tells Malcolm that before he can act, he must grieve:

I must also feel it as a man.

In this powerful scene, Shakespeare realistically portrays a strong, good man made weak with grief and despair.  But this grief is soon converted to action as he converts his grief to anger, and the conflict becomes external once again.

In Shakespeare's Macbeth, Lady Macbeth appears at first to be free of internal conflict, unless you consider her ambition and strong desire for power to be an internal conflict.  Her husband seems bothered by guilt concerning the assassination of Duncan, but she does not.  He obsesses over Duncan's blood on his hands, but she tells him that just a little blood will wash it, and all evidence against them, away. 

She is not as free from conflict as she might seem, though.  When she begs for the spirits to make her more like a man so she can follow through with the assassination, she reveals she has doubts about her own ruthlessness.  Then, when she has the opportunity to stab Duncan to death herself, she can't go through with it, because the sleeping Duncan reminds her of her father.  These details plant the seed for what happens later.

Lady Macbeth becomes overwhelmed by her guilt for the parts she plays in the killings of Duncan, Banquo, and Macduff's family.  Though she does not have anything directly to do with any of the murders except Duncan's, she certainly started the whole process of murder by shaming her husband into killing Duncan.  She becomes obsessed with guilt, and is ultimately destroyed by it when she commits suicide.  Her ambition collides with her conscience and her conscience wins, so to speak.

I'll let another editor tell you about Macduff.