Hamlet jokes about one actor’s new beard: “valenced” means “curtained” and “beard me” plays on the sense of “challenge me, defy me” (see the image of “Pluck[ing] off my beard” below).

This joke may or may not be addressed to the First Player; see Arden Shakespeare note.

Unequally matched, Pyrrhus drives at Priam, strikes wide in rage, but topples the frightened father [Priam] with the force of the wind from his formidable sword.

On the image of a sword’s mighty “whiff” toppling an opponent, the Arden Shakespeare (Third Series, p. 269) points to a passage in Christopher Marlowe and Thomas Nash’s play Dido and one in Edmund Spenser’s epic poem The Faerie Queene:

…And lightly lept from vnderneath the blow:
Yet so exceeding was the villeins powre,
That with the wind it did him ouerthrow…

“Why should he weep for Hecuba? He doesn’t even know Hecuba!”

Hamlet is appalled that an actor can show more emotion for a fictional character than he can show–or possibly even feel?–for his own dead father.

Hecuba is the legendary queen of Troy who appears in the passage the Player performed (at Hamlet’s request) above. More on her at Britannica.

Hecuba Blinding Polymestor, Giuseppe Maria Crespi, 18th century

Hamlet once again critiques and “directs” the characters around him, including the players themselves. He is like a representative of Shakespeare himself, who was the leader of his company of players. (And recall that Shakespeare had a son named Hamnet, and is said to have played the ghost of Hamlet senior…James Joyce made much of these parallels in Chapter 9 of Ulysses).

cleave…ear: split the audience’s ears.

appal the free: “horrify the innocent (those free of guilt), or make them turn pale with fear” [Arden Shakespeare].

Confound the ignorant: “discomfit, devastate those who are unaware (of the crime)” [Arden Shakespeare].

Notice the implications of the “motive/cue” metaphor. Hamlet compares himself to an actor who has all the motivation in the world, but can’t follow his cues–can’t act (in a double sense) accordingly.

His frustration at failing to follow his “cue for passion” suggests a deeper fear: that he lacks that passion to begin with.

brave: meaning either “courageous” or “admirable” (heavily sarcastic either way).

An instance of what Harold Bloom calls the “self-overhearing” that Shakespeare was particularly skilled at depicting. The self-conscious Hamlet “overhears” himself spewing insults and cries of vengeance, rather than doing anything, and feels suddenly absurd.

W. H. Auden believed that Hamlet wished to be a “creature of situation” like the heroes of Greek drama; instead he finds himself with almost too much power to think and choose for himself. Here he almost seems to be reminding himself of his situation for his own benefit–“This is who I am; therefore this is what I should do.”

a dear father murder’d: the First Folio has simply “a dear murdered”–perhaps an error, or perhaps “murdered” meant “murder victim.”

by…hell: The Arden Shakespeare notes:

Hamlet is either going for rhetorical inclusiveness, invoking the entire universe in his cause as he did when he asked whether he should couple hell to heaven and earth…or he is concerned whether the Ghost is ‘a spirit of health or goblin damned’…a topic to which he returns [later in the scene]. To be Prompted by hell would undercut the moral authority of his revenge.

“Heaven and hell” might also stand in for the good and evil aspects of avenging his father (duty to family vs. murder).

Mild curses. For a moment Hamlet’s disgust with words reduces him to inarticulate swearing and noise.

“Relative” means almost the opposite of what we’d expect here; Hamlet is seeking firmer, if not absolute, grounds for action. The Riverside Shakespeare (2nd ed., p. 1207) glosses: “closely related (to fact), i.e. conclusive.”