En esta clase, no es obligatorio hablar en voz alta.

Because clase is a feminine singular noun in Spanish, so the demonstrative has to agree with it:

• este = masculine singular
• esta = feminine singular

So:

• este libro
• esta clase

In modern Spanish, esta normally does not take an accent mark.

It usually means in this class or in this lesson/session, depending on context.

Spanish clase can refer to:

• a class session
• a school subject
• a course/class group

So En esta clase could mean:

• In this lesson
• In this class
• In this course, if the speaker means the class more generally

The exact meaning comes from the situation.

Because Spanish uses ser with qualities, definitions, rules, and general statements like this.

Obligatorio here means mandatory / required, which is being presented as a rule or general condition, so Spanish uses ser:

• Es obligatorio
• Es necesario
• Es importante

Using estar with obligatorio would sound unnatural here.

Because obligatorio is not describing clase. It is describing the action hablar en voz alta.

In this kind of structure, when an infinitive action is the thing being judged, Spanish normally uses the masculine singular form by default:

• Es obligatorio estudiar
• Es importante descansar
• No es necesario venir

Compare that with a sentence where the subject is a feminine noun:

• La asistencia no es obligatoria
• La participación oral no es obligatoria

There, the adjective agrees with the noun.

Because the infinitive in Spanish can act like a noun and refer to an action in a general way.

Here, hablar means something like speaking:

• hablar en voz alta = speaking out loud

After expressions such as:

• es obligatorio
• es necesario
• es importante

Spanish very often uses an infinitive to say what action is being talked about.

You could also say:

• No es obligatorio que hables en voz alta

But that version is more specific to you.

No. It means it is not required.

So the idea is:

• you do not have to speak out loud

It does not mean:

• you must not speak out loud

That difference is important.

Compare:

• No es obligatorio hablar en voz alta = it is not mandatory
• No está permitido hablar en voz alta = it is not allowed
• Está prohibido hablar en voz alta = it is forbidden

En voz alta is a fixed expression meaning out loud or aloud.

Literally, it is something like in a loud voice, but in normal use it often corresponds to aloud.

Examples:

• leer en voz alta = read aloud
• decir algo en voz alta = say something out loud

This is not exactly the same as alto.

• Hablar alto usually means to speak loudly
• Hablar en voz alta means to speak out loud / aloud

Sometimes the meanings overlap, but they are not always identical.

Normally, no. The standard expression is en voz alta.

So you should learn it as a set phrase:

• en voz alta = aloud
• en voz baja = quietly / in a low voice

Using a voz alta would sound non-standard in this context.

Not really. In Spanish, a short introductory phrase like En esta clase often appears without a comma:

• En esta clase no es obligatorio hablar en voz alta.

That is probably the more neutral version.

A comma can be used to mark a pause or add emphasis, but many Spanish writers would leave it out here. So the sentence with the comma is understandable, but without the comma is also very natural.

Yes. All of these are natural, but they are slightly different in tone.

• No es obligatorio hablar en voz alta = more formal, focused on rules or requirements
• No es necesario hablar en voz alta = not necessary
• No hace falta hablar en voz alta = no need to speak out loud; very common in everyday Spanish, including Spain

So if a teacher is stating a classroom rule, no es obligatorio works very well.

Because this sentence is a general statement, not one aimed at a specific person grammatically.

Spanish often leaves subjects unstated, especially in impersonal or general expressions.

So:

• No es obligatorio hablar en voz alta

means something like:

• Speaking out loud is not obligatory
• It is not obligatory to speak out loud

If the speaker wanted to address one person more directly, they might say:

• No es obligatorio que hables en voz alta

If speaking to a group in Spain:

• No es obligatorio que habléis en voz alta

Because obligatorio means mandatory / required, which is the meaning needed here.

• obligatorio = compulsory, mandatory
• obligado = obliged, forced, compelled

So:

• Es obligatorio llevar uniforme = Wearing a uniform is mandatory
• Estoy obligado a ir = I am obliged to go

In your sentence, the idea is about a rule, so obligatorio is the correct choice.