Does Shakespeare's Othello convey true psychological knowledge (knowledge about how human beings are likely to act or to react under certain circumstances or under the influence of ideologies or beliefs)—especially with regard to race and how an actual Moor at the time would behave if he went to Venice?

Although many literary critics contend that Shakespeare had no access to the teachings of modern cognitive science, one fact remains: he wrote for an audience he understood, and he leveraged a universal language shared by his audience.
Shakespeare understood an important fact about human nature: when pressed, many of us tend to make decisions from a place of fear. Our deepest vulnerabilities and insecurities surface when our sense of self is threatened.
Take Othello, for instance. On the surface, his power is obvious to all. He's both a Moorish prince and an appointed general in the Venetian Army. Additionally, he's the husband of a beautiful (white) woman from an upper-class background.
Despite this, Othello's deep insecurities about race and his sense of self bring about his ultimate downfall. Iago manages to manipulate all of Othello's fears to lead the latter into making increasingly disastrous choices as time progresses.
Consider this interaction between the two in act 3, scene 3:

OTHELLO
No, not much moved.
I do not think but Desdemona’s honest.
IAGO
Ay, there’s the point. As, to be bold with you,
Not to affect many proposèd matches
Of her own clime, complexion, and degree,
Whereto we see in all things nature tends—
Foh! One may smell in such a will most rank,
Foul disproportions, thoughts unnatural.
But—pardon me—I do not in position
Distinctly speak of her, though I may fear
Her will, recoiling to her better judgment,
May fall to match you with her country forms,
And happily repent.

Initially, Othello defends Desdemona. However, the wily Iago hints that Desdemona acted unnaturally when she turned away from men of her own "clime, complexion, and degree." He suggests that her "better judgment" rests upon her personal values, the ones she has chosen to keep suppressed and hidden. Iago suggests that Desdemona's "true self" will eventually emerge and lead her to regret choosing a dark Moor as her husband.
Here, Iago plays on Othello's secret fears. Even though Othello holds a privileged position in Venetian society, he understands that latent racism still exists. After all, he's still a Moor in an adopted country. Iago knows this, and he also knows that the husbands of his time (regardless of color) fear being cuckolded above all else.
In all of Iago's machinations against Othello, we see the themes of racism, jealousy, and the distinction between appearance and reality highlighted. Iago himself is a racist, but he hides this fact by projecting his racism onto others.
Here's an example: along with Roderigo (who pines after Desdemona), Iago tries to convince Brabantio that Othello, especially since he's black, will make an undesirable son-in-law. For his part, Iago characterizes Othello as an "old black ram" attempting to bed an innocent "white ewe." Whether Iago is merely projecting his own racism onto Brabantio or playing on the latter's latent racism is hotly debated among literary critics.
One fact remains, however: by manipulating other people's private fears and insecurities, Iago manages to bring about Othello's downfall and the death of the innocent Desdemona. This seems to imply that Shakespeare's play does convey knowledge about how human beings are likely to act or to react under certain circumstances or under the influence of ideologies or beliefs.