Ez az ellenőrzés elég.

When a demonstrative like ez (this) directly goes with a noun, Hungarian normally also uses the definite article:

• ez a könyv = this book
• az a ház = that house

Because ellenőrzés starts with a vowel, the article appears as az, not a. So:

• ez az ellenőrzés = this inspection / this check

So the pattern is normal Hungarian grammar, even though it looks unusual from an English point of view.

No. In this sentence, az is the definite article the, not the demonstrative that.

Hungarian has:

• ez = this
• az = that
• a / az = the

So in ez az ellenőrzés, the first word ez is the demonstrative, and the second word az is just the article required before the noun.

Because Hungarian usually leaves out the verb van (is) in the present tense, third person, in simple statements like this.

So:

• Ez az ellenőrzés elég. literally looks like This inspection enough. but it means This inspection is enough.

This omission is very common in Hungarian.

Compare:

• A ház nagy. = The house is big.
• Ez jó. = This is good.

But in other persons, Hungarian does use the verb:

• Elég vagyok. = I am enough.
• Elég vagy. = You are enough.

Here elég means enough or sufficient.

In this sentence it works as the predicate, so:

• Ez az ellenőrzés elég. = This check is enough.

A useful thing to know is that elég can also mean quite / fairly in other sentences:

• elég jó = quite good
• elég nehéz = fairly difficult

So the word is flexible, but here the meaning is clearly enough.

Ellenőrzés is a noun meaning something like:

• check
• checking
• inspection
• verification

The best English translation depends on context.

It is related to the verb ellenőriz, which means to check, to inspect, or to verify.

So:

• ellenőriz = to check
• ellenőrzés = checking / check / inspection

It is in the nominative, the basic dictionary form, with no extra ending.

In this sentence, ellenőrzés is the subject:

• Ez az ellenőrzés = this inspection / this check

If it were the object, it would change:

• ezt az ellenőrzést = this inspection (as a direct object)

So the form in your sentence is the plain subject form.

Because ez is the subject here, not the object.

Hungarian demonstratives change form depending on case:

• ez = this (subject/basic form)
• ezt = this (object form)

So:

• Ez az ellenőrzés elég. = This inspection is enough.
• Ezt az ellenőrzést kérem. = I want this inspection.

A very important pattern is that the demonstrative and the noun both show the case:

• ezt az ellenőrzést
• ebben az ellenőrzésben
• erről az ellenőrzésről

This agreement is a normal feature of Hungarian.

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

The neutral version is:

• Ez az ellenőrzés elég.

If you say:

• Elég ez az ellenőrzés.

that puts more focus on elég, something like:

• This inspection is enough
• This inspection will do

So the original sentence is a normal, neutral order.

It is grammatical and understandable. It can sound natural in the right context, especially when someone is deciding whether one check/inspection is sufficient.

Depending on context, Hungarian speakers might also say:

• Ez az ellenőrzés elég lesz. = This check will be enough.
• Ez már elég. = This is enough already.

So your sentence is fine, but real-life phrasing may vary depending on whether the speaker means is enough now, will be enough, or that is enough.

The stress is on the first syllable, as usual in Hungarian:

• EL-len-őr-zés

A few pronunciation notes:

• e is like a short e
• ő is a long Hungarian vowel that does not exist in standard English
• zs does not appear here as one letter pair; the word has z and then later s
• final s in Hungarian is pronounced like English sh

So the end of ellenőrzés sounds roughly like -zhaysh to an English speaker, though that is only approximate.

Also, ez az is pronounced smoothly together in speech, so the beginning may sound very connected.