Learn Hardcore Russian: Учёный читает книгу в библиотеке. - The scientist is reading a book in the library.

In Russian there are no articles like a or the. Nouns stand alone without a separate word to express definiteness or indefiniteness; context and word order carry that information.

What case is книгу, and why is it in that form?

This is the accusative singular of книга (book). Because книгу answers “What is being read?” (the direct object), feminine nouns ending in -a switch to -у in the accusative.

What case does в библиотеке show, and why use that case here?

в plus the prepositional case indicates location (“in the library”). библиотека becomes библиотеке in the prepositional singular for feminine nouns ending in -a, signaling “where” the action takes place.

Why is the verb читает used here?

читает is the third person singular present tense form of the imperfective verb читать (to read). Since учёный (“scientist”) is singular third person, the verb takes the ending -ет.

What is the aspect of читать, and how would a perfective form differ?

читать is imperfective—it describes an ongoing or habitual action (“is reading” or “reads regularly”). The perfective counterpart is прочитать, which focuses on completion (“to read through,” “to have read”).
Example: учёный прочитает книгу means “The scientist will (successfully) read the book (to the end).”

How is Учёный читает книгу в библиотеке pronounced and transliterated?

Pronunciation (IPA): [uˈt͡ɕɵnɨj t͡ɕɪˈtajet ˈknʲiɡu f bʲɪblʲɪɐˈtʲekʲɪ].
Transliteration: Uchyonyy chitayet knigu v biblioteke. Note that ё always indicates stress and is pronounced “yo.”

How would you ask “Where is the scientist reading the book?” in Russian?

Use the question word где (where):
Где учёный читает книгу?
Answer: В библиотеке (“In the library.”)

How do you form the feminine and plural forms of учёный?

• Feminine: учёная (ending -ая)
• Plural (all genders): учёные (ending -ые)
After that, they decline like adjectives/nouns of the same pattern.