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Shouldn't this be
Yesterday, the sun was hot.
Вчера, солнце было жарко.

I wrote the book "Who stole my eggs?".
Я написал книгу, "Кто крал мои яйца?".

I read the book "Who stole my eggs?"....

Maybe this is better.
Мне нужно написать письмо моему брату.

Sorry for the edits. I think this is the right way.

I need to write a letter to my brother.
Мне нужно писать писмо мой брату.

Here is my attempt. Don't kill me if I made a mistake. :D

Dogs and cats are very funny. They make good friends. They usually like food. I don't like their food, but they do.

Собаки и коты...