En esa asignatura hay doscientos estudiantes.

Because hay means there is / there are and is used to say that something exists or is present.

So:

• Hay doscientos estudiantes = There are two hundred students

By contrast, está/están is used more for saying where a specific person or thing is:

• Los estudiantes están en el aula = The students are in the classroom

A useful shortcut:

• hay = existence
• está/están = location of something specific

Also, hay does not change for singular or plural:

• Hay un estudiante
• Hay doscientos estudiantes

It stays hay in both cases.

In Spain, asignatura usually means a school/university subject or module, such as maths, history, chemistry, etc.

So En esa asignatura is something like:

• In that subject
• In that course
• sometimes In that class, depending on context

A native English speaker should know that asignatura is not always the same as a physical classroom session. It often refers to the academic subject itself.

Because esa means that, while esta means this.

• esta asignatura = this subject
• esa asignatura = that subject

Spanish demonstratives have to agree with the noun in gender and number:

• asignatura is feminine singular
• so the correct form is esa

Compare:

• ese libro = that book
• esa asignatura = that subject
• esos libros = those books
• esas asignaturas = those subjects

Here en means in.

• En esa asignatura = In that subject / In that course

Spanish often uses en where English uses in. It can refer to being within a subject area, class, place, or context.

Examples:

• En la universidad = At/In the university
• En matemáticas = In maths
• En esa asignatura hay examen = In that subject, there is an exam

After hay, Spanish normally does not use a definite article when you are simply saying that something exists.

So:

• Hay doscientos estudiantes = There are two hundred students

That is the normal structure.

If you said hay los estudiantes, that would sound wrong in standard Spanish.

Compare:

• Hay un profesor = There is a teacher
• Hay muchos libros = There are many books
• Hay doscientos estudiantes = There are two hundred students

You only use a definite article if the structure is different and you are talking about specific known people or things in another way.

Because in Spanish, the hundreds are normally written as single words:

• cien
• doscientos
• trescientos
• cuatrocientos
• etc.

So doscientos is the standard spelling for two hundred.

A few examples:

• doscientos estudiantes = two hundred students
• trescientos euros = three hundred euros

You would not normally split it as dos cientos.

Yes. The hundreds from doscientos onward agree in gender with the noun.

Here we have:

• doscientos estudiantes

That is the masculine/general form.

Compare:

• doscientos libros = two hundred books
• doscientas personas = two hundred people

So if the noun is clearly feminine, you use -as:

• doscientas alumnas
• trescientas casas

With estudiantes, the masculine form is often used as the general/default form for a mixed or unspecified group.

Because that is the normal order in Spanish:

• number + noun

So:

• doscientos estudiantes
• tres libros
• veinte profesores

This is similar to English:

• two hundred students

It would not normally be estudiantes doscientos.

Estudiante is a noun that can refer to either a male or a female student. It is a common-gender noun.

So you can say:

• el estudiante = the male student
• la estudiante = the female student

In the plural:

• los estudiantes can mean the male students or the students in a mixed group
• las estudiantes means the female students

In your sentence, there is no article, so estudiantes just means students.

Both are possible, but starting with En esa asignatura puts the topic first.

So:

• En esa asignatura hay doscientos estudiantes = emphasis on in that subject
• Hay doscientos estudiantes en esa asignatura = emphasis first on the fact that there are two hundred students

Spanish is fairly flexible with word order, especially when moving a phrase to the front for focus or context.

A simple pronunciation guide is:

en EH-sa ah-seeg-nah-TOO-rah eye dos-SYEN-tos es-too-DYAN-tes

A few notes for Spain:

• esa: the s is a clear s
• hay sounds like eye
• ci in doscientos is pronounced with the Spain th sound in much of Spain: roughly doth-SYEN-tos
• estudiantes has the stress on dian: es-tu-DIAN-tes

A more Spain-like approximation would be:

en EH-sa ah-seeg-nah-TOO-ra eye doth-SYEN-tos es-too-DYAN-tes

Sometimes, but not always.

• asignatura = the academic subject/module
• clase = the class session, or sometimes the class as a group

So if you mean the subject itself, asignatura is better.

Examples:

• Me gusta esa asignatura = I like that subject
• Tengo clase de historia = I have history class

If you replace asignatura with clase, the meaning may shift slightly depending on context.

The noun phrase inside it is already plural: doscientos estudiantes.

If you wanted to make asignatura plural too, you would say:

• En esas asignaturas hay doscientos estudiantes = In those subjects there are two hundred students

Notice the changes:

• esa → esas
• asignatura → asignaturas

But hay stays the same. That is very important:

• hay works for both singular and plural.