A vízhőmérséklet jó.

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

So:

A vízhőmérséklet jó.
literally looks like The water temperature good.
but it means The water temperature is good.

This omission is completely normal.

But in other persons or tenses, the verb appears:

• A vízhőmérséklet jó volt. = The water temperature was good.
• A vízhőmérséklet jó lesz. = The water temperature will be good.
• A vízhőmérséklet jó? = Is the water temperature good?

A is the Hungarian definite article, meaning the.

Hungarian has two forms:

• a before a consonant
• az before a vowel

Since vízhőmérséklet begins with v, a consonant, the correct form is a:

• a vízhőmérséklet = the water temperature

If the next word started with a vowel, you would use az instead.

Yes, it is one word. Hungarian very often writes compound nouns as a single word.

vízhőmérséklet is made up of:

• víz = water
• hőmérséklet = temperature

So it literally means water-temperature.

This kind of compounding is very common in Hungarian, and it often corresponds to English noun + noun combinations.

A rough pronunciation guide:

• a = short aw / uh
• víz ≈ veez
• hő has a long ő, a rounded vowel that English does not really have
• mér ≈ mare but with a pure long vowel, not an English diphthong
• sék ≈ shayk with a pure é
• let ≈ let
• jó ≈ yoh

A few useful sound notes:

• í, é, ó, ő are long vowels.
• zs is pronounced like the s in measure.
• Stress in Hungarian normally falls on the first syllable of the word: VÍZhőmérséklet.

A rough overall approximation is:

uh VEEZH-her-mayr-shayk-let yoh

Not perfect, but close enough to get started.

Here, jó is not directly modifying the noun. It is the predicate adjective: it tells you what the water temperature is.

So:

• A vízhőmérséklet jó. = The water temperature is good.

But if you want good to directly modify water temperature, then it comes before the noun:

• jó vízhőmérséklet = good water temperature

So the difference is:

• A vízhőmérséklet jó. = complete sentence
• jó vízhőmérséklet = noun phrase, not a full sentence by itself

Yes. That is also correct.

Both are grammatical, but the word order changes the emphasis a little:

• A vízhőmérséklet jó. = neutral statement; topic first, then comment
• Jó a vízhőmérséklet. = more emphasis on good, often like The water temperature is good / The water temperature is fine

Hungarian word order is strongly connected to information structure and emphasis, not just grammar.

So both are possible, but they do not always feel exactly the same in context.

Because the subject is singular, and the adjective is in its basic predicate form.

Here:

• vízhőmérséklet = singular
• so jó stays singular too

If the subject were plural, the predicate adjective would usually also be plural:

• A vízhőmérsékletek jók. = The water temperatures are good.

So in your sentence, jó is simply the correct singular form.

Both can mean something like The water temperature is good, but the structure is different.

• A vízhőmérséklet jó.
  This uses a compound noun: water temperature.

• A víz hőmérséklete jó.
  This literally means The water's temperature is good or The temperature of the water is good.

The second version uses a possessive structure:

• a víz = the water
• hőmérséklete = its temperature / the temperature of it

Both are natural, but the compound vízhőmérséklet is often a bit more compact and dictionary-like, while a víz hőmérséklete can sound slightly more specific or analytic depending on context.