It was a time when all women were men, at least on the stage. Boys and men played the female parts. The "nurses" and other character parts were the Mrs. Doubtfires of the Elizabethan and Jacobean theatre. Lady MacBeth would have been Tootsie.
He worked his way from the groundlings up, holding the horses, and no doubt passing the hat. He acted his parts, he collaborated with other writers, his writing style changed with the times.
When he achieved some success he was roundly criticized by the glittering literary elites for being a common man (not university educated), and for being a jack-of-all trades within the entertainment industry.
He wrote plays, poems, sonnets, sagas, but he also (with others) tore down a theatre that they had constructed on rented land when a landlord tried to take advantage, and rebuilt the Globe theatre. One might compare him to PT Barnum.
No stranger to political patronage and sponsorship, he was a Lord Chancellor's Man during the reign of Queen Elizabeth I, and then a King's Man.
His Histories could have been compared to the sometimes scurrilous sagas about Royal Families, loosely based on someone's truth, and heavily laden with political brown-proboscising, to show first Gloriana's ancestral enemies and then the foes of James I and VI in a bad light, and to portray their royal forebears in the best possible taste.
Apart from Histories, he wrote Comedies, Tragedies, Tragi-Comedies, and so-called Problem plays. He borrowed other people's material, and pleased his crowds with jingoism, and the prejudices of his day, but interestingly the union between Othello and Desdemona was not remarkable for anything except the violent and tragic jealousy of Othello.
He wrote of Romans, Frenchmen, Englishmen of all degrees, Egyptians, Moors, Venetians, Italians, Scots, Fairies, Witches, Wizards, indecisive and dastardly Danes... and more; of lovers, soldiers, kings, ghosts, murderers, lawyers, rogues and rebels, horny teenagers, and victims of prejudice.
As for his education, he would have been strictly schooled in English grammar (no bad thing), and the latin classics. One interesting note is that he acted in a play called Sejanus His Fall. Today, we would call it Sejanus's Fall, but the apostrophe-s was not in vogue at the time.
Shakespeare is possibly the most influential writer in the English language, and there is so much more to his life, work and legacy than his pallor, gender, and nationality.
Credits to Wikipedia: https://en.wikipedia.org/wiki/William_Shakespeare
All the best,