Az erkölcsi kérdés fontos.

Hungarian has two forms of the definite article:

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

Because erkölcsi begins with a vowel, you say az erkölcsi kérdés.

Compare:

• a fontos kérdés = the important question
• az erkölcsi kérdés = the moral/ethical question

This is similar to English a / an, but it applies to the definite article instead.

In Hungarian, the verb to be is usually omitted in the present tense, third person when the sentence is simple and descriptive.

So:

• Az erkölcsi kérdés fontos. = The moral question is important.

But in other persons, you do use the verb:

• Fontos vagyok. = I am important.
• Fontos vagy. = You are important.
• Fontosak. = They are important.
  or more fully: Ők fontosak.

In the past or future, the verb also appears:

• fontos volt = was important
• fontos lesz = will be important

Erkölcsi is an adjective meaning moral or ethical.

It comes from the noun erkölcs, which means morality or ethics, plus the adjective-forming ending -i:

• erkölcs = morality, morals
• erkölcsi = moral, ethical

This -i ending is very common in Hungarian for making adjectives.

In this sentence, fontos is the predicate adjective, so it comes after the subject phrase:

• Az erkölcsi kérdés = the moral question
• fontos = important

This word order is very normal and neutral in Hungarian.

So the sentence structure is basically:

• [subject] + [adjective predicate]

That gives:

• Az erkölcsi kérdés fontos.

Yes. Hungarian word order is flexible, but changing it often changes the emphasis.

For example:

• Az erkölcsi kérdés fontos.
  Neutral: The moral question is important.

• Fontos az erkölcsi kérdés.
  This puts more emphasis on important, as if answering What is important?

So the original sentence is the most neutral, straightforward version.

Yes, kérdés can mean more than just a spoken or written question.

Depending on context, it can mean:

• question
• issue
• matter
• problem in some contexts

So Az erkölcsi kérdés fontos could be understood as:

• The moral question is important
• The ethical issue is important

The exact English wording depends on context.

In Hungarian, adjectives usually do not agree with the noun the way they do in many Indo-European languages.

So:

• erkölcsi stays erkölcsi
• fontos stays fontos

They do not change for grammatical gender, because Hungarian has no grammatical gender, and they do not change here for case or number.

Examples:

• az erkölcsi kérdés = the moral question
• az erkölcsi kérdések = the moral questions

Notice that kérdés changes to kérdések, but erkölcsi stays the same.

Yes. The whole sentence is a basic subject-predicate sentence, so the subject az erkölcsi kérdés is in the nominative form.

There is no special ending here showing another case.

• kérdés = question
• kérdést = question (accusative, as a direct object)

Since the sentence means The moral question is important, not I see the moral question or something similar, the nominative form is used.

A rough guide for English speakers:

• az ≈ oz or az, with a short vowel
• erkölcsi ≈ ER-kol-chee
• kérdés ≈ KAYR-daysh
• fontos ≈ FON-tosh

A few useful sound notes:

• ö and ő are front rounded vowels; English does not have exact equivalents
• cs sounds like ch in church
• s in Hungarian sounds like English sh
• é is like a long ay
• á is like a broad long a

So fontos is pronounced more like FON-tosh, not fon-tos in English spelling.

It can be a natural phrase, but it is not a completely frozen expression. It is simply:

• erkölcsi = moral / ethical
• kérdés = question / issue

So together it means moral question or ethical issue in a normal, compositional way.

You can build similar phrases freely in Hungarian:

• politikai kérdés = political question/issue
• jogi kérdés = legal question/issue
• személyes kérdés = personal question

So erkölcsi kérdés is natural, but not especially idiomatic or irregular.