A tanárnő részletes választ ad, ha a diák pontosan kérdez.

Yes. Tanárnő means female teacher.

• tanár = teacher
• nő = woman

So tanárnő is specifically a woman teacher. If the speaker does not want to mention gender, Hungarian often just uses tanár.

A is the Hungarian definite article, meaning the.

• a tanárnő = the teacher
• a diák = the student

Hungarian uses a / az much like English uses the, but sometimes also in general statements about familiar roles, so this sentence can sound like either a specific situation or a general rule about the teacher and the student.

Also note:

• a is used before consonants
• az is used before vowels

Because választ is the accusative form of válasz.

• válasz = answer
• választ = answer, as a direct object

Here it is the direct object of ad:

• választ ad = gives an answer

In Hungarian, direct objects usually take the ending -t.

Because in Hungarian, when an adjective directly modifies a noun, the case ending usually appears only on the noun, not on the adjective.

So:

• részletes válasz = detailed answer
• részletes választ = detailed answer (as object)

The adjective részletes stays the same, while válasz gets the accusative ending -t.

Hungarian can do both.

• választ ad = gives an answer
• válaszol = answers / replies

So this sentence could also be expressed with válaszol, but választ ad is a very natural expression and emphasizes the answer itself.

Compare:

• A tanárnő részletes választ ad. = The teacher gives a detailed answer.
• A tanárnő részletesen válaszol. = The teacher answers in detail.

The meaning is similar, but the wording is slightly different.

Because Hungarian often omits egy when the object is indefinite and the phrase is a common verb+noun combination.

So:

• részletes választ ad = gives a detailed answer

This is very natural Hungarian.

If you say:

• egy részletes választ ad

that is also possible, but it puts a bit more weight on a / one detailed answer.

This is about Hungarian definite vs. indefinite verb conjugation.

Here the object részletes választ is indefinite, so Hungarian uses the indefinite verb form:

• ad = gives

If the object were definite, Hungarian would usually use the definite form:

• A tanárnő a választ adja. = The teacher gives the answer.

So in your sentence:

• részletes választ = an indefinite answer
• therefore ad, not adja

Ha means if.

So:

• ha a diák pontosan kérdez = if the student asks precisely / asks clearly

The comma is there because Hungarian normally separates clauses with a comma, including clauses introduced by ha.

So the structure is:

• main clause: A tanárnő részletes választ ad
• subordinate clause: ha a diák pontosan kérdez

Because Hungarian distinguishes between two different ideas that English often expresses with ask.

• kérdez = ask a question / inquire
• kér = ask for something / request something

In this sentence, the student is asking questions, so kérdez is the correct verb.

Compare:

• A diák kérdez. = The student asks questions.
• A diák segítséget kér. = The student asks for help.

Here pontosan means something like precisely, accurately, or clearly.

It comes from:

• pontos = precise, exact
• pontosan = precisely, exactly

In the sentence, it describes how the student asks:

• pontosan kérdez = asks precisely / asks clearly and specifically

So the idea is that the teacher gives a detailed answer when the student asks in a precise way.

No. Hungarian word order is flexible, and changing it often changes emphasis more than basic meaning.

This version is a natural, neutral one:

• A tanárnő részletes választ ad, ha a diák pontosan kérdez.

You could also say:

• Ha a diák pontosan kérdez, a tanárnő részletes választ ad.

That puts the if-clause first, which is also very natural.

So the word order is not random, but it is not as rigid as in English.

Grammatically, it is present tense:

• ad = gives
• kérdez = asks

But in Hungarian, present tense is often used for general truths, habits, and even future-like conditions.

So this sentence can mean:

• The teacher gives a detailed answer if the student asks precisely.
• or, in a natural English translation, The teacher will give a detailed answer if the student asks precisely.

The exact English wording depends on context.

It can be understood either way, depending on context.

Because Hungarian uses the definite article here:

• a tanárnő
• a diák

the sentence may refer to:

1. a specific teacher and student already known in the conversation, or
2. a general teacher-student situation, almost like the teacher ... the student ...

So context decides whether it is specific or more general.