Az orosz látogató olvas.

Both a and az mean the. Hungarian chooses between them based on the sound that follows:

• a before a consonant sound
• az before a vowel sound

Since orosz begins with o, the correct form is az orosz.

This is similar in function to English a/an, but it applies to the definite article instead.

In Hungarian, adjectives normally come before the noun they describe, just as in English.

So:

• orosz látogató = Russian visitor

Here orosz is acting as an adjective meaning Russian, and látogató is the noun visitor.

Hungarian adjectives usually do not change form to match the noun in gender or basic singular use.

That is very different from many European languages. Hungarian has:

• no grammatical gender
• no masculine/feminine adjective agreement

So orosz stays orosz.

Whether the noun is masculine, feminine, or something else is irrelevant, because Hungarian does not mark that kind of gender.

Here it is a noun, meaning visitor.

It comes from the verb látogat, meaning to visit, so learners sometimes notice that it looks like a participle or verbal form. But in this sentence, az orosz látogató clearly functions as a noun phrase: the Russian visitor.

In other contexts, forms like this can feel more adjective-like, but here the meaning is clearly visitor.

Because the subject in Hungarian is usually in the nominative, and the nominative often has no ending at all.

So látogató appears in its basic dictionary form.

Hungarian often marks the object more clearly than the subject. For example:

• látogató = visitor, as subject
• látogatót = visitor, as direct object

So in your sentence, the lack of an ending is normal for a subject.

This is a very common Hungarian question, because Hungarian verbs have two main conjugation patterns:

• indefinite
• definite

Olvas is the indefinite 3rd person singular form.

It is used when:

• there is no direct object stated, or
• the object is indefinite/general

That fits this sentence, because we are simply told that the visitor is reading, without saying exactly what.

If there were a specific definite object, you would normally use the definite form:

• Az orosz látogató olvassa a könyvet. = The Russian visitor is reading the book.

So olvas is correct here.

It can mean either, depending on context.

Hungarian present tense often covers both:

• reads
• is reading

So Az orosz látogató olvas. could mean:

• The Russian visitor reads.
• The Russian visitor is reading.

In natural translation, English usually chooses the version that best fits the situation.

If Hungarian wants to make the ongoing right now meaning clearer, it can add a word like éppen:

• Az orosz látogató éppen olvas. = The Russian visitor is reading right now.

Yes. Hungarian word order is flexible, but different orders often change the focus or emphasis.

Az orosz látogató olvas. is a neutral statement:
The Russian visitor is reading.

If you change the order, you may create a different emphasis. For example:

• Olvas az orosz látogató.

This can sound more like:

• The Russian visitor is reading
  perhaps in contrast to doing something else

So the original order is the most neutral, straightforward one.

A simple pronunciation guide is:

• Az → roughly awz
• orosz → roughly OR-os
• látogató → roughly LAA-to-ga-too
• olvas → roughly OL-vawsh

A few very useful spelling notes:

• Hungarian stress is usually on the first syllable of each word.
• sz sounds like English s
• s sounds like English sh
• á is a long vowel
• ó is also a long vowel

So one especially important contrast here is:

• orosz ends in sz = s
• olvas ends in s = sh