Az alku után a vevő megnézi a bakelitlemezt és az ékszert.

Után is a postposition, which means Hungarian puts it after the noun, not before it like English usually does.

So:

• az alku = the bargain / the negotiation / the deal-making
• az alku után = after the bargaining / after the negotiation

This is different from English after the bargain, where after comes first. In Hungarian, many such words come after the noun:

• ebéd után = after lunch
• munka után = after work

So Az alku után is a time phrase meaning after the bargaining/negotiation.

Hungarian often uses the definite article a / az where English would say the.

• vevő = buyer
• a vevő = the buyer

In this sentence, it refers to a specific buyer, so a vevő is natural.

Hungarian articles work like this:

• a before most consonant sounds
• az before vowel sounds

So:

• a vevő
• az ékszer
• az alku

This is a very common learner question.

The verb base is néz = to look, to watch.

Adding meg- often gives the idea of doing something completely, having a look at, or checking/looking over. So:

• néz = look/watch
• megnéz = look at, inspect, check out

In this sentence, megnézi means something like looks at it / examines it.

Also, megnézi is the definite conjugation form, because the verb has definite objects:

• a bakelitlemezt
• az ékszert

So the form is not just about the prefix meg-, but also about Hungarian verb conjugation.

Because Hungarian verbs have two main conjugation patterns:

• indefinite conjugation
• definite conjugation

You use the definite form when the verb has a specific, definite object.

Here the objects are definite:

• a bakelitlemezt = the vinyl record
• az ékszert = the piece of jewelry / the jewelry item

So Hungarian uses:

• megnézi = he/she looks at it / examines it

Compare:

• Néz egy lemezt. = He/she is looking at a record.
• Megnézi a lemezt. = He/she looks at the record.

So the -i here is part of the 3rd person singular definite conjugation.

Because they are the direct objects of the verb, and Hungarian marks direct objects with -t.

• bakelitlemez → bakelitlemezt
• ékszer → ékszert

This -t is the accusative ending.

English usually does not mark direct objects on nouns, but Hungarian often does.

Examples:

• olvas egy könyvet = reads a book
• látom a házat = I see the house
• vesz egy almát = buys an apple

So in your sentence, the buyer is examining what?

• a bakelitlemezt
• az ékszert

That is why both nouns take the accusative ending.

This is because of the form of the definite article:

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

So:

• a bakelitlemezt because bakelitlemez starts with b
• az ékszert because ékszer starts with é, a vowel

This is similar to English a and an, but not exactly the same in usage. Hungarian chooses between a and az based on the following sound.

Yes, it is one word, and Hungarian very often forms compounds this way.

• bakelit = bakelite / vinyl-like older material term
• lemez = disc / record

Together:

• bakelitlemez = vinyl record

Hungarian likes compound nouns, and they are usually written as one word when they form a single concept.

In the sentence, it appears as:

• a bakelitlemezt

That includes:

• a = the
• bakelitlemez = vinyl record
• -t = accusative marker

Yes, Hungarian word order is more flexible than English, but it is not random. Word order often shows topic, focus, and what the speaker wants to emphasize.

This sentence is neutral and natural:

• Az alku után a vevő megnézi a bakelitlemezt és az ékszert.

It begins with a time phrase:

• Az alku után = after the bargaining

Then comes the topic:

• a vevő = the buyer

Then the verb and objects.

You could rearrange parts for emphasis, but the meaning or emphasis may shift. For example, putting something before the verb can highlight it.

So the given word order is a normal, straightforward way to say it.

Mostly yes.

• és = and

Here it connects two direct objects:

• a bakelitlemezt és az ékszert

So the buyer examines:

1. the vinyl record
2. the jewelry item

This works very much like English and.

Hungarian often repeats the article before each noun in a list when each one is a definite noun phrase.

So:

• a bakelitlemezt és az ékszert

is fully natural and standard.

English can do something similar:

• the record and the jewelry

Hungarian usually sounds better with the article repeated when both nouns are definite and separate items.

Megnézi is:

• 3rd person singular
• present tense
• definite conjugation

So it means:

• he/she looks at it
• he/she examines it

In your sentence, the subject is a vevő = the buyer, so:

• a vevő megnézi = the buyer examines / looks at

Hungarian does not need a separate word for he/she here, because the verb ending already shows the person.

It is singular.

• ékszer = a piece of jewelry / jewel / ornament
• ékszert = the accusative singular form

English jewelry is often an uncountable noun, so this can feel tricky for learners. In Hungarian, ékszer is a normal countable noun. Depending on context, it may mean:

• a piece of jewelry
• a jewel
• an item of jewelry

So this sentence is talking about one specific jewelry item.

In Hungarian, the main stress is almost always on the first syllable of the word.

So you would stress:

• AL-ku
• U-tán
• VE-vő
• MEG-né-zi
• BA-ke-lit-le-mezt
• ÉK-szert

That first-syllable stress rule is very helpful and very regular in Hungarian.

They are just two forms of the same definite article: the.

Use:

• a before consonant sounds
• az before vowel sounds

So:

• az alku because alku starts with a
• az ékszert because ékszer starts with é
• a vevő because vevő starts with v

So there is no difference in meaning between a and az. The choice depends only on pronunciation.