A diák szendvicset kér a kávézóban.

Hungarian has two forms of the definite article: a and az.

• a is used before consonant sounds: a diák (d- is a consonant)
• az is used before vowel sounds: az ember, az iskola
  It’s based on pronunciation, not spelling rules like in English.

All three are possible, but they differ in nuance:

• szendvicset kér: “some/a sandwich” in a general, non-specific sense (very common in Hungarian)
• egy szendvicset kér: explicitly one sandwich / “a sandwich” with emphasis on “one”
• a szendvicset kéri/kér: “the sandwich” (a specific, known sandwich)

So leaving out the article is a normal way to keep the object non-specific.

Hungarian has two main verb conjugations in the present tense:

• indefinite (alanyi) when the object is not definite or not specific
• definite (tárgyas) when the object is definite/specific (often with a/az, a name, a pronoun like azt, etc.)

Here the object is szendvicset (no definite article), so Hungarian typically uses the indefinite form: kér.

Compare:

• A diák szendvicset kér. (indefinite: some/a sandwich)
• A diák kéri a szendvicset. (definite: the sandwich)

-ban/-ben is the inessive case, meaning in/inside a place.

Which one you use depends on vowel harmony:

• -ban after back vowels (a, á, o, ó, u, ú): kávézóban
• -ben after front vowels (e, é, i, í, ö, ő, ü, ű): e.g., üzletben

Since kávézó contains back vowels (á, ó), you get kávézóban.

Using a here often implies a particular café (or the relevant one in the situation): in the café / in the coffee shop (we mean).

You can omit it, but the feel changes:

• A diák … a kávézóban. = in the café (more specific/grounded)
• A diák … kávézóban. = in a café / in cafés (more generic, less anchored)

In everyday speech, both occur, but a kávézóban is very natural.

Hungarian word order is flexible and often reflects what you want to emphasize.

This sentence is a neutral, common order (topic → new info):

• A diák (topic) + szendvicset
  • kér
    • a kávézóban

Other natural options with different focus:

• A diák a kávézóban kér szendvicset. (emphasis on where the requesting happens)
• Szendvicset kér a diák a kávézóban. (emphasis on what is requested)

The ending tends to carry “afterthought” or background info, but it’s very context-dependent.

No—kér means request / ask for something.

Hungarian typically uses:

• kér = ask for, request: szendvicset kér
• kérdez = ask a question: kérdez valamit (e.g., kérdez egyet / kérdez valamit)

So kér fits because the sentence is about requesting an item.

Yes. Hungarian often omits the subject if it’s clear from context because the verb ending carries person/number information (though in 3rd person singular, it’s not as informative as in 1st/2nd person).

So you could say simply:

• Szendvicset kér a kávézóban.
  That would still be grammatical; it just relies more on context for who.

A few common variations:

• Plural subject: A diákok szendvicset kérnek a kávézóban.
  (kérnek = 3rd plural, indefinite)
• Plural object (still non-specific): A diák szendvicseket kér a kávézóban.
  (szendvicseket = plural accusative)
• If the object is definite (known sandwiches), you’d typically use the definite conjugation accordingly, e.g. A diákok kérik a szendvicseket (context-dependent).