Learn Hardcore Russian: Студентка читает книгу в библиотеке. - The student female is reading a book in the library.

In the sentence we need a conjugated verb form that agrees with the subject студентка (3rd person singular, she). For the verb читать (to read), the present tense is:

я читаю – I read
ты читаешь – you read (informal)
он/она/оно читает – he/she/it reads
мы читаем – we read
вы читаете – you read (plural/formal)
они читают – they read

Since студентка = она (she), we use читает: Студентка читает…

Why is книга changed to книгу?

Книга is the dictionary form (nominative case, book).
In the sentence, книгу is the direct object of the verb читает (she reads what? – a book).

In Russian, direct objects usually take the accusative case. For a feminine noun ending in -а, the accusative singular ends in -у:

книга (nom.) → книгу (acc.)
машина (car) → машину
газета (newspaper) → газету

So читает книгу = reads a book / is reading a book.

Why is it в библиотеке and not в библиотека?

Библиотека (library) appears here after the preposition в meaning in (location).

With в meaning in/at (location, not movement), Russian uses the prepositional case. For a feminine noun ending in -а, the prepositional singular typically ends in -е:

библиотека (nom.) → в библиотеке (prep.) – in the library
школа → в школе – in/at school
комната → в комнате – in the room

So в библиотеке literally means in the library.

What’s the difference between в библиотеке and в библиотеку?

The preposition в can be used with two different cases, giving two different meanings:

в + prepositional (где? where?) – location
- в библиотеке – in the library (where she is)
в + accusative (куда? where to?) – movement / direction
- в библиотеку – to the library (where she is going)

Compare:

Студентка читает книгу в библиотеке. – The (female) student is reading a book in the library.
Студентка идёт в библиотеку. – The (female) student is going to the library.

Could the word order be different, like В библиотеке студентка читает книгу?

Yes. Russian word order is more flexible than English. All of these are grammatically correct:

Студентка читает книгу в библиотеке.
Студентка в библиотеке читает книгу.
В библиотеке студентка читает книгу.
Книгу студентка читает в библиотеке.

The basic meaning stays the same, but word order affects emphasis and what is treated as “new” information”:

Starting with Студентка… emphasizes who is doing the action.
Starting with В библиотеке… emphasizes where this is happening.
Putting книгу first gives extra focus to the book as the object.

For a neutral statement, Студентка читает книгу в библиотеке is the most standard.

How would the sentence change if the student were male?

You would only change the noun for student:

Студент читает книгу в библиотеке. – The (male) student is reading a book in the library.

The verb читает, the object книгу, and в библиотеке stay the same, because they do not depend on the subject’s gender here.

How do I say “The student is reading books in the library” (plural books)?

You need the plural of книга:

Singular: книга (nom.), книгу (acc.)
Plural: книги (nom.), книги (acc. for inanimate nouns)

So the sentence becomes:

Студентка читает книги в библиотеке. – The (female) student is reading books in the library.
Студент читает книги в библиотеке. – The (male) student is reading books in the library.

Note: for inanimate nouns in the plural, nominative and accusative forms are the same.

Can Студентка читает книгу в библиотеке mean both “is reading” (right now) and “reads” (habitually)?

Yes. Russian does not have a separate present continuous form like English is reading.

The form читает can mean:

She is reading a book in the library (right now), or
She reads a book in the library (regularly, as a habit).

Context or additional words show which meaning is intended:

Сейчас студентка читает книгу в библиотеке. – Right now the student is reading a book in the library.
Каждый день студентка читает книгу в библиотеке. – Every day the student reads a book in the library.

Why is читает used and not something like прочитала? What’s the difference in aspect?

Читать is imperfective: it focuses on the process or repeated action.
Прочитать is perfective: it focuses on the completed result.

In the present:

Only the imperfective has a true present tense: читает – is reading / reads
The perfective прочитать does not have a real present; its “present” form refers to the future:
- она прочитает – she will read (will finish reading)

For past:

Она читала книгу в библиотеке. – She was reading / used to read a book in the library.
Она прочитала книгу в библиотеке. – She read the book in the library (and finished it).

In your sentence, читает describes the action of reading itself, not the completed result.

How do I pronounce the words in Студентка читает книгу в библиотеке and where is the stress?

Stress (capitalized vowel) and a rough guide:

студЕнтка – stu-DYENT-ka
читАет – chi-TA-yet
кнИгу – KNEE-goo (the г is like English g in go)
в – like English v (often very short)
библиотЕке – beeb-lee-a-TYE-ke (the е in the stressed syllable is like “ye” in “yes”)

Main stresses:

студЕнтка
читАет
КНигу (stress on и)
библиотЕке

Russian has no articles. How do I know if it’s “a book” or “the book” in читает книгу?

Russian does not use a / an / the, so книгу by itself can be translated as a book or the book, depending on context:

If you’re mentioning it for the first time or it’s not specific → usually a book.
If both speaker and listener already know which book it is → usually the book.

So:

Студентка читает книгу в библиотеке.
- could be The student is reading a book in the library, or
- The student is reading the book in the library, depending on context.

The Russian sentence itself does not force one choice.

How would I turn this sentence into a question like “What is the student reading in the library?”

You mainly change the intonation and add a question word; word order can stay similar or shift a bit for emphasis. Common options:

Что студентка читает в библиотеке? – What is the student reading in the library?
Что читает студентка в библиотеке? – (very common, neutral)
В библиотеке что читает студентка? – In the library, what is the student reading? (focus on the place)

Что = what. The verb form читает stays the same; Russian doesn’t use auxiliary verbs like does for questions.