Itt látszik a hegy.

No. Látszik and lát are related, but they are not the same.

• lát = to see
• látszik = to be visible, to be seen, sometimes to seem / to appear

So:

• Látom a hegyet. = I see the mountain.
• Látszik a hegy. = The mountain is visible. / The mountain can be seen.

In Itt látszik a hegy, látszik means is visible or can be seen.

Because a hegy is the subject of the sentence, not the direct object.

With látszik, the thing that is visible is treated as the subject:

• A hegy látszik. = The mountain is visible.

But with lát, the thing seen is the object, so it takes -t:

• Látom a hegyet. = I see the mountain.

So:

• a hegy = nominative, subject
• a hegyet = accusative, direct object

Hungarian often leaves out subject pronouns when they are not needed, and in this sentence there is already a full verb: látszik.

So the structure is simply:

• itt = here
• látszik = is visible / can be seen
• a hegy = the mountain

There is no need for a separate word meaning it.

Also, there is no separate word for is here because látszik is already the verb of the sentence. It is not a noun/adjective sentence like A hegy magas (The mountain is tall).

Hungarian word order is flexible, and the beginning of the sentence often shows what is being highlighted.

Starting with itt puts attention on the location:

• Itt látszik a hegy. = Here, the mountain is visible. / The mountain can be seen here.

This is natural if you are pointing out a place.

A different order can change the emphasis:

• A hegy itt látszik. = The mountain is visible here.

That version sounds more like the mountain is the topic, while itt is the important new information.

So the original sentence emphasizes here.

A is the definite article, meaning the.

Hungarian has two forms of the definite article:

• a before consonants
• az before vowels

So:

• a hegy = the mountain
• az erdő = the forest

Because hegy starts with a consonant sound, the correct form is a.

In this sentence, yes: itt means here.

But it helps to compare it with other related words:

• itt = here, at this place
• ide = to here
• innen = from here

Examples:

• Itt van. = It is here.
• Gyere ide! = Come here!
• Innen látszik a hegy. = The mountain can be seen from here.

So itt is the right choice when you mean location at a place.

Yes, in some contexts it can.

For example:

• Úgy látszik, esni fog. = It seems it will rain.

But in Itt látszik a hegy, that is not the natural meaning. Here it clearly means:

• The mountain is visible here
• The mountain can be seen here

So the context tells you which meaning is intended.

It is the present tense, third person singular form of the verb látszik.

That matches the singular subject a hegy:

• a hegy = the mountain
• látszik = is visible

So literally, the grammar is something like:

• here + is visible + the mountain

You can think of látszik as the normal dictionary form you will often meet first.

A rough English-friendly guide is:

itt LAAT-sik a hedy

A few useful pronunciation points:

• itt has a short i, but the tt is long, so the final consonant is held a little.
• á is a long vowel, like a longer aa sound.
• sz is pronounced like English s.
• In látszik, the t + sz combination gives a ts sound.
• gy in hegy is a soft sound that does not exist exactly in English; hedy is only an approximation.

Hungarian stress normally falls on the first syllable of each word:

• ITT
• LAAT-szik
• a
• HEGY