Isn't piszesz also correct as that also means "you write"
Yes, it's the singular 'you' write. "piszecie" is plural.
Why is it not "pismo"?
"Pismo" may indeed be some formal, official letter, but it seems safer not to add it, as it's a false friend with Russian - where it just means any letter. And there's nothing wrong with calling an official letter "list".
Dlaczego: "piszesz literę" jest źle?
Cóż... no fakt, nie da się takiej interpretacji wykluczyć. Dodałem.
For others: This is "You are writing a letter" as in "You are writing one letter from the alphabet".