A lakás az üzlet felett van.

They mean the same thing. Hungarian has two forms of the definite article:

• a before a consonant sound: a lakás
• az before a vowel sound: az üzlet

So this works a bit like a/an in English, except both forms mean the.

Lakás usually means apartment or flat. It can also mean a dwelling in a broader sense, but in everyday use it most often refers to an apartment.

If you wanted house, the usual word would be ház.

Because felett is a postposition, not a preposition.

English says:

• above the shop

Hungarian says:

• the shop above
• az üzlet felett

Hungarian often puts these location words after the noun:

• mellett = next to / beside
• alatt = under
• előtt = in front of
• mögött = behind
• felett = above

It is a separate word.

So in az üzlet felett, the word üzlet does not take an extra ending here; the spatial relationship is expressed by the postposition felett.

This is different from forms like:

• üzletben = in the shop
• üzlethez = to the shop

Those are case endings attached directly to the noun.

That is a very common question.

Hungarian often omits van in the present tense in sentences like:

• A lakás nagy. = The apartment is big.
• A lakás szép. = The apartment is nice.

But with location, van is normally kept:

• A lakás az üzlet felett van.
• A kulcs az asztalon van. = The key is on the table.

So here van is needed because the sentence tells you where the apartment is.

That is the normal, neutral word order here.

Hungarian word order is not as rigid as English word order. It often works by topic + comment.

In this sentence:

• A lakás = the topic, what we are talking about
• az üzlet felett van = the comment, what we are saying about it

Putting van at the end sounds natural in a plain statement of location.

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

• Az üzlet felett van a lakás.
  This puts more attention on the location.

Yes. felett and fölött are both used and both mean above / over.

So these are both possible:

• A lakás az üzlet felett van.
• A lakás az üzlet fölött van.

The difference is mostly one of usage preference, style, or regional habit, not basic meaning.

You would say:

A lakás nincs az üzlet felett.

The negative of van is usually nincs in this kind of sentence.

So Hungarian does not normally say nem van here.

A few useful pronunciation points:

• Stress is always on the first syllable of each word.
• s is pronounced sh in Hungarian.
• á is a long vowel.
• ü is a front rounded vowel, like German ü or French u.

A rough guide:

• lakás ≈ lah-kaash
• üzlet ≈ uez-let (there is no exact English sound for ü)
• felett ≈ feh-lett
• van ≈ vawn

A more exact pronunciation is approximately:

• A lakás az üzlet felett van.
  [ɒ ˈlɒkaːʃ ɒz ˈyzlɛt ˈfɛlɛtː vɒn]

Yes, üzlet can mean shop/store or business, depending on context.

In this sentence, because something is physically located above it, the natural meaning is shop or store:

• az üzlet felett = above the shop

So here it refers to the place, not to business in the abstract sense.