Questions & Answers about Папа сидит на диване и читает книгу.
Why is the word for book spelled книгу here instead of its dictionary form книга?
This is the Accusative case in action! Because the book is the direct object of the sentence—the thing receiving the action of being read—its ending changes. For feminine nouns ending in -а like книга, the ending changes to -у to become книгу.
Диван (sofa) is also an inanimate object in this sentence. Why doesn't it take the Accusative case like the book does?
Because the sofa isn't the direct object receiving an action. Instead, it follows the preposition на (on) to show location. When answering the question "where?", на requires the Prepositional case. That is why the masculine noun диван gets an -е ending to become на диване.
The word папа ends in -а. Shouldn't it change to папу in the Accusative case?
It would, but only if Dad were the one receiving the action (for example, if someone were reading a book about Dad). In this sentence, Dad is the subject—he is the one actively doing the sitting and reading. Because he is the subject, папа stays in the standard Nominative case.
The translation says "is sitting" and "is reading". Do сидит and читает represent a special continuous tense in Russian?
No, Russian doesn't have a separate tense for "is doing" something right now. The standard present tense verbs сидит and читает can mean "sits / reads" or "is sitting / is reading". You just choose the English translation that sounds most natural based on what is happening in the scene.