I read a book about making food.
Я прочитал книгу о готовить еде.
"Прочитать" means that you read it and finished the book, "читать" is just that you were reading it. "готовить" is a verb. You can't say "о готовить" even though in english it is "about making" and making is a verb. In russian you write the noun. Еде shouldn't be written like this. "To prepare food"- "Готовить еду".

On Thursday I will buy three hats.
В четверг я покупаю три шапкы
"покупаю" means you are buying it at the moment. "Шапки" is right because after к you cannot put ы.

Please, gitell me when I can buy skis.
Пожалуйста, Сказай меня где, я можно купить лыжи.
"Сказай" is just incorrect, correct is "Скажите". and after this word you put "Мне."
You can say: Скажите, пожалуйста, где можно купить лыжи?

They are writing him a letter.
Они ему пишут письмо
"Они пишут ему письмо" just sounds better.