Habla bajo en la biblioteca.

Here, habla is the affirmative tú command of hablar.

• hablar = to speak
• (tú) habla = speak

So the sentence is giving an instruction to one person in an informal way.

A useful comparison:

• Tú hablas = you speak
• Habla = speak!

Even though habla can also mean he/she speaks or you speak (formal, usted), in this sentence it is understood as a command because of the context.

Because affirmative tú commands usually use the third-person singular present form:

• hablar → habla
• comer → come
• vivir → vive

So:

• Habla bajo = Speak quietly

By contrast, no hables is the negative tú command:

• No hables tan alto = Don’t speak so loudly

It can mean more than one thing grammatically:

• (tú) habla = speak!
• él/ella habla = he/she speaks
• usted habla = you speak (formal)

In this sentence, it is understood as a command because the whole sentence sounds like an instruction: Habla bajo en la biblioteca.

If you wanted a formal command to one person, you would normally say:

• Hable bajo en la biblioteca.

Because bajo here is being used as an adverb, not an adjective.

It describes how someone speaks:

• hablar bajo = to speak quietly / softly

Since it is not describing a noun, it does not change for gender or number.

Compare:

• una voz baja = a low/quiet voice
  Here baja is an adjective describing voz, which is feminine.
• habla bajo = speak quietly
  Here bajo works adverbially, so it stays bajo.

Yes, it is understandable and natural enough, but Spanish also often uses:

• Habla en voz baja = Speak in a low voice / Speak quietly
• Baja la voz = Lower your voice
• Habla más bajo = Speak more quietly

For many learners, en voz baja is especially useful because it is very common and clear.

En usually means in, inside, or at, depending on context.

So:

• en la biblioteca = in the library

It tells you where the action happens.

Examples:

• Estoy en casa = I’m at home
• Estudia en la universidad = He/She studies at the university
• Habla bajo en la biblioteca = Speak quietly in the library

Because in Spanish, nouns often need a definite article where English may or may not use one.

• la biblioteca = the library

Biblioteca is a feminine singular noun, so it takes la.

You could also say en una biblioteca if you mean in a library rather than in the library.

No. In standard Spanish, h is silent.

So habla is pronounced roughly like abla.

This is true in words like:

• hola
• hombre
• hablar

The b sound in habla is the one you hear, not the h.

A simple approximate pronunciation is:

• bee-blee-oh-TEH-ka

In Spain, the c before a is a normal k sound:

• biblioteca → -teca = -teh-ka

Also, the stress falls on te:

• bib-lio-TE-ca

Yes. If you want to speak formally to one person, use the usted command:

• Hable bajo en la biblioteca.

Compare:

• Habla bajo = Speak quietly. informal, one person
• Hable bajo = Speak quietly. formal, one person

In Spain, informal tú is very common, but formal usted is used in more polite or distant situations.

In Spain, to give an informal command to more than one person, use vosotros:

• Hablad bajo en la biblioteca.

For a formal plural command, use ustedes:

• Hablen bajo en la biblioteca.

So the main forms are:

• Habla bajo = one person, informal
• Hable bajo = one person, formal
• Hablad bajo = more than one person, informal in Spain
• Hablen bajo = more than one person, formal

Yes, that is grammatically fine and means Don’t speak loudly in the library.

But it is slightly different in tone:

• Habla bajo = positive instruction
• No hables alto = negative instruction

Both are natural, but the positive version often sounds a bit smoother or more direct for this kind of situation.