A napijegy drága.

Because Hungarian usually leaves out the present-tense verb to be in the 3rd person singular (and often plural) when the predicate is a noun or an adjective.

So:

• A napijegy drága. = The day ticket is expensive.

Literally, it looks like:

• The day ticket expensive.

But in Hungarian, that is perfectly normal.

You do use the verb van / vannak in other situations, for example in the past:

• A napijegy drága volt. = The day ticket was expensive.

or with 1st/2nd person:

• Drága vagyok. = I am expensive.

A is the definite article, so it means the.

• a napijegy = the day ticket

Hungarian has two forms of the definite article:

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

So here it is a napijegy because napijegy begins with n, a consonant.

Because napijegy starts with a consonant sound.

Hungarian chooses the article like this:

• a busz = the bus
• az autó = the car

So:

• a napijegy is correct
• az napijegy is not correct

It is a compound word:

• napi = daily
• jegy = ticket

So napijegy literally means daily ticket, often translated more naturally as day ticket or day pass.

The first part, napi, comes from:

• nap = day
• -i = an ending that makes it mean something like daily or related to the day

Because Hungarian very often writes this kind of expression as a compound noun.

English may use two words:

• day ticket

But Hungarian commonly joins them:

• napijegy

This is very normal in Hungarian. Many everyday words are built this way.

Because here drága is not directly describing the noun inside a noun phrase. It is the predicate: it tells you something about the subject.

So:

• A napijegy drága. = The day ticket is expensive.

But if you put the adjective before the noun, it becomes an ordinary noun phrase:

• a drága napijegy = the expensive day ticket

So the position changes the structure:

• A napijegy drága. → full sentence
• A drága napijegy... → noun phrase, not a complete sentence by itself

Not for gender, because Hungarian has no grammatical gender.

So you do not have to worry about masculine/feminine/neuter adjective forms.

In this sentence:

• napijegy = singular
• drága = singular form

If the subject is plural, Hungarian often uses a plural predicate adjective:

• A napijegyek drágák. = The day tickets are expensive.

So there can be number marking, but not gender agreement.

Yes. Hungarian word order is fairly flexible, but different orders create different emphasis.

Neutral statement:

• A napijegy drága.

If you say:

• Drága a napijegy.

that puts more focus on drága — something like:

• The day ticket is expensive
• or It’s the day ticket that’s expensive

So the basic meaning stays similar, but the emphasis changes.

A rough guide:

• a ≈ short aw
• napijegy ≈ NOH-pee-yedgy
• drága ≈ DRAA-gaw

A few important points:

• Hungarian stress is usually on the first syllable of each word.
• á is a long vowel.
• The j sounds like English y.
• The final sound in jegy is gy, a Hungarian sound that is softer than English g.

A more careful pronunciation is approximately:

• [ɒ ˈnɒpiˌjɛɟ ˈdraːɡɒ]

You do not need to master the IPA immediately, but it can help if you want precise pronunciation.

No. Drága can also mean dear or beloved, depending on context.

For example:

• Ez drága. = This is expensive.
• Drága barátom = my dear friend

In A napijegy drága, the meaning is clearly expensive.

Yes, but it changes the nuance.

• A napijegy drága. = The day ticket is expensive / can also sound like a general statement about the day ticket option
• Egy napijegy drága. = A day ticket is expensive or One day ticket is expensive

So:

• a = the
• egy = a/an or one

In many general statements, Hungarian often uses the definite article where English might use a or a bare plural.

It is in the nominative form, which is the basic dictionary form.

There is no special ending here because it is the subject of the sentence:

• A napijegy drága.

If it were the direct object, it would usually take the accusative ending:

• napijegyet

For example:

• Veszek egy napijegyet. = I’m buying a day ticket.

So this sentence uses the plain subject form: napijegy.