Valahányszor az olvasóterembe megyek, folyóiratot olvasok.

Valahányszor means whenever, every time that, or more literally as many times as.

In this sentence, it introduces a repeated situation:

Valahányszor az olvasóterembe megyek, folyóiratot olvasok.
= Whenever I go to the reading room, I read a journal / magazine.

It is a conjunction that starts a subordinate clause, similar to English whenever.

It can sound a little more formal or literary than some other everyday ways of expressing the same idea.

Hungarian has two forms of the definite article:

• a before consonant sounds
• az before vowel sounds

Because olvasóterembe begins with the vowel o, Hungarian uses az:

• az olvasóterembe

Compare:

• a könyvtárba = into the library
• az iskolába = into the school

The ending -be is the illative case ending. It means movement into something.

So:

• olvasóterem = reading room
• olvasóterembe = into the reading room

With megyek (I go), Hungarian normally uses a directional ending like this, because the action involves movement toward and into a place.

A useful contrast:

• olvasóterembe megyek = I am going into / to the reading room
• olvasóteremben vagyok = I am in the reading room

So -be is for motion inward, while -ben is for being inside.

Hungarian usually leaves out the subject pronoun if the verb ending already makes the subject clear.

Here:

• megyek = I go
• olvasok = I read

The endings already show first person singular, so én is not necessary.

If you do add én, it usually gives emphasis or contrast:

• Én folyóiratot olvasok. = I read a journal. / As for me, I read a journal.

So the version without én is the normal neutral one.

Yes. Megyek is the 1st person singular present tense form of the verb menni (to go).

This verb is somewhat irregular, so learners often have to memorize its forms.

Some present-tense forms are:

• megyek = I go
• mész = you go
• megy = he/she/it goes
• megyünk = we go
• mentek = you all go
• mennek = they go

So megyek simply means I go.

Because it is the direct object of the verb olvasok (I read), and Hungarian marks direct objects with the accusative ending.

So:

• folyóirat = journal / periodical
• folyóiratot = a journal / journal (as object)

In this sentence, the thing being read is the object, so Hungarian adds the accusative ending.

This is one of the most common patterns in Hungarian:

• könyv → könyvet
• újság → újságot
• folyóirat → folyóiratot

This is a very common Hungarian question. Hungarian verbs can use two different conjugations:

• indefinite conjugation
• definite conjugation

Here, the object folyóiratot is indefinite / non-specific, so Hungarian uses the indefinite verb form:

• olvasok = I read

If the object were definite, you would use olvasom:

• A folyóiratot olvasom. = I am reading the journal.
• Ezt a folyóiratot olvasom. = I am reading this journal.

So in your sentence:

• folyóiratot olvasok = I read a journal / journals / periodicals
• not olvasom, because the object is not definite

Because Hungarian often uses a bare noun as an indefinite object, especially in general or habitual statements.

So:

• folyóiratot olvasok can mean something like I read a journal, I read journals, or I do journal-reading, depending on context.

If you said:

• egy folyóiratot olvasok = I am reading a / one journal

that would sound more like a single specific-but-unknown item.

If you said:

• a folyóiratot olvasom = I am reading the journal

that would be definite.

So the version in the sentence is natural for a repeated, general action.

Not necessarily. In this sentence, the present tense expresses a habitual or repeated action.

So:

• Valahányszor az olvasóterembe megyek, folyóiratot olvasok.

means a general pattern:

• Whenever I go to the reading room, I read a journal.

Hungarian often uses the plain present tense for habits, routines, and repeated actions, just as English does in sentences like:

• Whenever I go there, I read.
• Every morning I drink coffee.

Not exactly in every context.

Folyóirat usually means periodical, journal, or sometimes magazine, depending on context. It can sound a bit more formal than English magazine.

Possible related words:

• folyóirat = periodical / journal / magazine
• újság = newspaper
• magazin = magazine (often more directly like the English word)

So if the translation you saw says magazine, that is possible, but journal or periodical may be closer in some contexts.

Not completely. Hungarian word order is flexible, but it is strongly connected to topic and focus.

This sentence has a natural, neutral structure:

• Valahányszor az olvasóterembe megyek, folyóiratot olvasok.

That sounds like a straightforward statement: first the whenever clause, then the main clause.

In the main clause, folyóiratot olvasok is also neutral and natural.

You can change word order in Hungarian, but doing so usually changes emphasis. So learners should treat this sentence as a good normal model, not as the only possible order.

Because valahányszor az olvasóterembe megyek is a subordinate clause, and Hungarian normally separates such clauses with a comma.

So the structure is:

• Valahányszor az olvasóterembe megyek,
  subordinate clause
• folyóiratot olvasok.
  main clause

This is similar to English punctuation in a sentence like:

• Whenever I go to the reading room, I read a journal.

So the comma is standard and expected here.