Ez komoly helyzet.

Literally, it is:

Ez = this
komoly = serious
helyzet = situation

So the structure is basically This serious situation, but in natural English the sentence means This is a serious situation.

Hungarian often leaves out the present-tense is in this kind of sentence.

Because in Hungarian, the present-tense third-person form of to be is usually omitted when a sentence simply identifies or describes something with a noun or adjective.

So:

Ez komoly helyzet. = This is a serious situation.

But in other persons, Hungarian does use the verb:

Én fáradt vagyok. = I am tired.
Te fáradt vagy. = You are tired.

And Hungarian also uses van in other kinds of sentences, especially for location or existence:

Itt van. = It is here.

Hungarian often omits the indefinite article egy in predicate noun phrases, even where English would normally use a/an.

So Ez komoly helyzet is completely natural.

You can also say:

Ez egy komoly helyzet.

That is also correct and natural. Adding egy makes the noun phrase more explicitly like English a serious situation, while leaving it out can sound a bit more direct or categorical.

Here, ez stands on its own and means this or this thing. It is the subject of the sentence.

So the sentence is structured like:

Ez = the thing being talked about
komoly helyzet = what is being said about it

This is different from ez a helyzet, where ez directly modifies the noun and means this situation.

So:

Ez komoly helyzet. = This is a serious situation.
ez a helyzet = this situation

Because Hungarian adjectives normally come before the noun they describe, just as in English.

So:

komoly helyzet = serious situation
jó ötlet = good idea
nagy ház = big house

That part is very straightforward for English speakers.

Yes.

Ez komoly. means This is serious.

That version uses just the adjective komoly.
In Ez komoly helyzet, the speaker uses a full noun phrase, serious situation, which sounds a bit more specific and concrete.

So the difference is roughly:

Ez komoly. = This is serious.
Ez komoly helyzet. = This is a serious situation.

Yes, you could say Komoly helyzet ez.

Ez komoly helyzet is the more neutral order.
Komoly helyzet ez is more marked and gives extra emphasis to komoly helyzet.

A rough English feeling might be:

Ez komoly helyzet. = neutral statement
Komoly helyzet ez. = This is a serious situation indeed / Now this is a serious situation

Hungarian word order is often influenced by focus and emphasis, not just grammar.

Because if Hungarian wanted to say this serious situation as one noun phrase, it would normally use the article a after the demonstrative:

ez a komoly helyzet

That is the normal Hungarian pattern for this + noun.

So:

ez a komoly helyzet = this serious situation
Ez komoly helyzet. = This is a serious situation.

That little a makes a big difference.

A simple pronunciation guide is:

Ez — like ez with a short e
komoly — roughly KO-mo(y)
helyzet — roughly HEHY-zet, with ly sounding like y

Stress in Hungarian normally falls on the first syllable of each word:

EZ KOmoly HELYzet

One extra detail: in connected speech, the z in ez may sound devoiced before the k of komoly, so it can sound a bit like es komoly helyzet. The spelling does not change, only the pronunciation.