Did Edward de Vere write Hamlet?
No. For one thing, the First Folio printing of Hamlet has many minor changes to the play dialogue, as compared to the Second Quarto printing of 1604-5. Many of those changes give every appearance of being authorial, and they can be reasonably interpreted as occurring after the Second Quarto printing. It would not have been possible for the Earl to have made changes after the Second Quarto was printed, because he died in 1604.