A vevő és az árus egymásra néznek.

Hungarian has two forms of the definite article:

• a before a consonant
• az before a vowel

So:

• a vevő because vevő starts with v
• az árus because árus starts with á

It works a bit like choosing between a and an in English, although Hungarian does it only by sound at the beginning of the next word.

Because Hungarian normally repeats the definite article before each noun in a coordination like this.

So a vevő és az árus is the natural standard way to say the customer and the vendor.

Repeating the article makes it clear that both nouns are separate definite nouns. In sentences like this, that is the normal pattern.

They are the subjects of the sentence, so they are in the basic subject form, which is the nominative. In Hungarian, the nominative usually has no ending.

So:

• vevő = buyer/customer
• árus = vendor/seller

No extra ending is needed here because they are simply the ones doing the action.

Because together they make a compound subject:

• a vevő és az árus = the customer and the vendor

That means two people, so Hungarian uses a plural verb.

So:

• néz = he/she looks
• néznek = they look

This is the same basic idea as in English: The customer and the vendor look at each other, not looks.

Egymásra is made up of:

• egymás = each other / one another
• -ra = a suffix meaning roughly onto / onto it / at it, depending on the verb

So egymásra literally looks like onto each other, but with néz it means at each other.

This is a very common Hungarian pattern: the verb and the suffix go together as a unit.

Because the verb néz often connects with -ra / -re when it means look at someone or something.

Examples of the same pattern:

• rám néz = looks at me
• az égre néz = looks at the sky
• egymásra néznek = they look at each other

So this is not a random ending. It is the form this verb commonly uses in this meaning.

Here -nek is the 3rd person plural present tense ending of the verb in the indefinite conjugation.

Breakdown:

• néz- = the verb stem, look
• -nek = they in the present tense

So néznek means they look.

It is indefinite because there is no direct object here. The sentence uses egymásra, which is a suffixed form, not a direct object.

Because Hungarian usually does not need an explicit subject pronoun if the verb ending already shows who is doing the action.

So instead of saying something like they look, Hungarian can simply say:

• néznek

The ending already tells you it is they.

That is very common in Hungarian. Subject pronouns are often left out unless they are needed for emphasis or contrast.

They are close, but not exactly the same.

• egymásra néznek is the most natural way to say they look at each other
• egymást nézik is more like they are watching each other or they are looking at each other as direct objects

There is also a grammar difference:

• egymásra néznek uses the indefinite verb form néznek
• egymást nézik uses the definite verb form nézik, because egymást is a direct object

So the sentence you were given uses the more idiomatic expression for a mutual glance.

No, Hungarian word order is fairly flexible. The version you have is a neutral, natural sentence.

It roughly works like this:

• A vevő és az árus = topic / what we are talking about
• egymásra néznek = what happens

You can change the order, but the emphasis changes. For example:

• Az árus és a vevő egymásra néznek.
  Same basic meaning, just the nouns are reversed.

• Egymásra néz a vevő és az árus.
  This can sound more like bringing the action itself to the front.

So the meaning stays similar, but the information structure and emphasis can shift.