These are two questions, and their answers are largely independent of each other.
First, while Macbeth appears to be a tragic hero, his claim to the title is deeply flawed. Like a tragic hero, he is a high, admirable character at the beginning of the narrative, who seems to suffer from a single character defect -- his excessive ambition. He is brought down by the action of external forces (the prediction of the witches) exploiting this "tragic flaw," and is thus ruined. His weakness to ambition is something many share and can appreciate, and so his career and failure can arouse pity and fear in the audience. However, Macbeth lacks one key component of the tragic hero -- the final realization of the true situation and acceptance of his own responsibility in bringing it about (the Greek term is anagnorisis). Failure does not bring him new knowledge. It merely turns him into a species of nihilist, questioning the value of life in general. In the end, he dies blaming the witches, not himself:
And be these juggling fiends no more believed,
That palter with us in a double sense;
That keep the word of promise to our ear,
And break it to our hope. (Act V, Scene 8)
What this means is that his story lacks the essential conclusion to a true tragedy, the katharsis or "purging" that fully resolves the pity and fear the audience feels. Macbeth's problem is simply removed, not resolved, and so the play is not properly considered a tragedy in the classic sense.
The inversion of the characters of Macbeth and Lady Macbeth comes about through their changing attitudes towards the actions needed to take and keep power. At the beginning, it is Lady Macbeth who is all for murdering Duncan. She even turns the willingness to do the deed into a proof of how Macbeth feels about their relationship:
Was the hope drunk
Wherein you dress'd yourself? hath it slept since?
And wakes it now, to look so green and pale
At what it did so freely? From this time
Such I account thy love. (Act I, Scene 7)
Macbeth himself is worried, not so much about divine judgment, but about the precedent he will set by murdering a superior (Act I, Scene 7). He hesitates repeatedly, to the point that Lady Macbeth fears he has failed to do the deed:
The attempt and not the deed
Confounds us. Hark! I laid their daggers ready;
He could not miss 'em. Had he not resembled
My father as he slept, I had done't. (Act II, Scene 2)
The last line here indicates, though, that Lady Macbeth is not as strong as she pretends to be. After the murder, Macbeth himself becomes steadily sterner, while she begins to fall apart from suppressed remorse. When Macbeth has Banquo murdered, he does not tell her beforehand (Act III, Scene 2), and in fact she is already falling into a depression:
Nought's had, all's spent,
Where our desire is got without content:
'Tis safer to be that which we destroy
Than by destruction dwell in doubtful joy. (Act III, Scene 2)
We see little of her after the banquet scene until her guilt-filled sleepwalking and the final news of her suicide, but neither are surprising developments. The steady and relentless accumulation of crimes has overcome her:
The thane of Fife had a wife: where is she now? --
What, will these hands ne'er be clean? (Act V, Scene 1)
Her character has collapsed under the tension, while Macbeth's has hardened. He goes down fighting; she kills herself.
The tragedy of Macbeth is the tragedy of a self-divided man, a split-personality, a man who knows what is fair and what is foul, and yet unable to smother the foul in him, unable to prevent it from spoiling the precious fair for which he is so admired.
Macbeth is not that absolutely noble as the bleeding seargent portrays him in act1 sc.2. The way he reacts to the advances of the Witches in act1 sc.3 sufficiently suggests that he has a pre-existing seed of evil hibernating in the soil of his mind. His decision to fore-run King Duncan on the plea of making necessary arrangements for the King's visit to his castle, and his aside,'Stars, hide your fires!/Let not light see my black and deep desires...' further strengthen our suspicion of the presence of the virus of evil ambition in the psychological system of Macbeth.
Macbeth's letter with which Lady Macbeth appears also smacks of his 'burning desire' to become the king of Scotland. The letter immediately triggers off a dangerous volition in Lady Macbeth to stand by her husband's wish by curbing her natural self with unnatural cruelty obtainable from the dark spirits 'that tend on mortal thoughts'.
Lady Macbeth changes herself from act1 sc.6; she most deceptively plays the role of an all-caring hostess, whereas Macbeth remains unsettled, out of sight. Macbeth's long soliloquy with which act1 sc.7 begins clearly reveals the dilemma of the self-divided man. Macbeth is afraid of being punished in this world itself if he kills the good old King for no other reason but the fulfilment of his 'vaulting ambition'. The over-heated imagination of Macbeth produces the hallucination of a phantom dagger; Macbeth is terribly disturbed in the scene of Duncan's murder to look at his bloody hands; Macbeth reaches the climax of fear in the Banquet scene when the ghost of Banquo appears to shake his 'gory locks' at Macbeth.
Macbeth then meets the Witches to know more about his future. The three apparitions deceive Macbeth by their equivocations to seal the doom of a man caught between 'yesterdays' and 'tomorrows', a man with an imaginative conscience giving in to foul ambition and passing to defeat and termination. Lady Macbeth suffers from guilt and turns into a sleep-walker.
In Macbeth, both the usurper-king and his accomplice in crime are thus tragic characters who fall victims to unlawful ambition and self-sacrificing passion.