A főétel rendkívül finom.

A is the definite article in Hungarian, so here it means the.

A few useful points:

• a is used before consonant sounds
• az is used before vowel sounds

So:

• a főétel = the main course
• az étel = the food

Unlike English, Hungarian does not use a/an with a/az. The indefinite article is egy.

In Hungarian, the verb to be is often left out in the present tense, especially in third person singular and plural when the predicate is a noun, adjective, or adverb.

So:

• A főétel rendkívül finom. literally looks like The main course extremely delicious.
• But the natural English translation includes is.

Compare:

• Én fáradt vagyok. = I am tired.
• Te fáradt vagy. = You are tired.
• Ő fáradt. = He/She is tired. ← no van

So in your sentence, the missing is is completely normal.

Főétel is a compound word:

• fő = main, principal
• étel = food, dish

So főétel literally means main dish or main course.

Hungarian forms many compound nouns this way, so this is a very useful pattern to notice.

Rendkívül is an adverb meaning extremely, exceptionally, or remarkably.

It strengthens the adjective finom.

So:

• finom = delicious / tasty
• rendkívül finom = extremely delicious

It is a fairly strong and somewhat formal or polished word. In everyday speech, people might also say:

• nagyon finom = very delicious / very tasty
• iszonyúan finom = insanely delicious
• rettenetesen finom = terribly / extremely delicious

Because rendkívül is an adverb modifying the adjective finom.

This works similarly to English:

• extremely delicious
• very good
• really nice

In Hungarian, adverbs that modify adjectives usually come before the adjective:

• nagyon jó = very good
• rendkívül érdekes = extremely interesting
• meglepően finom = surprisingly tasty

So rendkívül finom is the normal word order.

Finom often means tasty, delicious, or nice-tasting, especially with food.

In this sentence, that is clearly the meaning.

But finom can also have other senses depending on context, such as:

• delicate
• subtle
• fine
• gentle

For example:

• finom illat = a delicate / pleasant smell
• finom mozdulat = a delicate movement
• finom por = fine dust

So it is a flexible adjective, but with food it usually means tasty or delicious.

A rough pronunciation guide for an English speaker is:

• A ≈ short aw
• főétel ≈ foe-ay-tel, but with a rounded vowel in fő
• rendkívül ≈ rend-kee-vool, again with rounded vowels
• finom ≈ fee-nom

A few important pronunciation notes:

• ő and ű are long rounded vowels that English does not really have
• é is like a long ay
• í is like a long ee
• Stress in Hungarian is always on the first syllable of the word:
  • FŐétel
  • RENDkívül
  • FInom

So the sentence has this stress pattern:

• A FŐétel RENDkívül FInom.

Because it is the subject of the sentence, and subjects in Hungarian are normally in the nominative case, which usually has no ending.

So the basic dictionary form appears here:

• főétel = main course

If it had another grammatical role, it might take an ending:

• A főételt kérem. = I’d like the main course.
  Here főételt has the accusative ending -t because it is the object.

So in your sentence, the lack of an ending is normal.

Yes. Hungarian word order is quite flexible, and changing it often changes the focus or emphasis, not just the basic meaning.

Your sentence:

• A főétel rendkívül finom.

This is a neutral statement.

Other possibilities:

• Rendkívül finom a főétel.
  This puts more emphasis on how delicious it is.
• Finom a főétel.
  Simpler: The main course is tasty.

So word order in Hungarian is not as fixed as in English. The version you have is natural and straightforward.

Yes, absolutely.

• A főétel nagyon finom. = The main course is very delicious / very tasty.
• A főétel rendkívül finom. = The main course is extremely delicious.

The difference is mainly intensity and style:

• nagyon = very; very common and everyday
• rendkívül = extremely / exceptionally; stronger and a bit more formal or elegant

So both are correct, but rendkívül sounds more emphatic and polished.