Az itatótál tele van.

Yes. Az is the definite article, meaning the.

Hungarian has two forms of the definite article:

• a before a word that starts with a consonant
• az before a word that starts with a vowel

Since itatótál begins with i, the sentence uses az itatótál.

Examples:

• a kutya = the dog
• az alma = the apple

Itatótál is a compound noun.

It is made up of:

• itató = something used for giving drink / watering
• tál = bowl

So itatótál is literally something like drinking bowl or watering bowl, depending on context. In natural English, it might be water bowl, drinking bowl, or pet bowl.

Hungarian forms many nouns this way by combining smaller words into one longer word.

In Hungarian, tele van is the normal way to say is full.

• tele = full
• van = is

So literally it looks like full is, but together it means is full.

This is a very common Hungarian pattern:

• tele van = is full
• üres by itself often means empty, but tele usually appears with van when making a full sentence

Examples:

• A pohár tele van. = The glass is full.
• A zsák tele van almával. = The bag is full of apples.

That is normal Hungarian word order here.

Hungarian often puts the descriptive part first and the verb after it:

• Az itatótál tele van.

This is the most neutral way to say The bowl is full.

Hungarian word order is flexible, but it is not random. Different orders can change emphasis.

For example:

• Az itatótál tele van. = neutral statement
• Tele van az itatótál. = stronger focus on full

So the version you have is a standard, natural sentence.

It behaves a lot like an adjective in meaning, because it describes a state: full.

However, learners often remember it as part of the fixed expression tele van rather than treating it exactly like a simple English-style adjective.

So the safest practical approach is:

• learn tele van = is full
• learn tele valamivel = full of something

Example:

• A tál tele van vízzel. = The bowl is full of water.

Usually no, not if you mean The bowl is full.

Teljes means complete, entire, or full in a different sense. It is not normally used for a container being full of something.

So:

• Az itatótál tele van. = correct for The bowl is full.
• teljes would sound wrong or unnatural here

Use tele for containers, spaces, and things filled with something.

You usually use tele van plus a noun in the instrumental ending -val / -vel.

Example:

• Az itatótál vízzel tele van.
• more naturally: Az itatótál tele van vízzel.
• = The bowl is full of water.

Here:

• víz = water
• vízzel = with water / full of water

Hungarian often uses the same case ending where English uses with or of, depending on the expression.

More examples:

• A zsák tele van homokkal. = The bag is full of sand.
• A szoba tele van emberekkel. = The room is full of people.

Hungarian adjectives do not agree with nouns the way they do in many Indo-European languages.

So there is no masculine/feminine/neuter agreement, and no singular/plural agreement in this kind of sentence.

That means:

• a tál tele van = the bowl is full
• a tálak tele vannak = the bowls are full

Notice that tele stays the same. The verb changes:

• van = singular is
• vannak = plural are

It would be:

• Az itatótálak tele vannak. = The bowls are full.

Changes:

• itatótál → itatótálak = bowl → bowls
• van → vannak = is → are

The article stays az, because itatótálak still begins with a vowel sound.

Not always, but in this sentence it is natural and normal.

• Az itatótál tele van. = The bowl is full.

If you remove the article:

• Itatótál tele van.

that usually sounds incomplete or unnatural unless you are speaking in a special context, such as notes, labels, headlines, or very telegraphic speech.

So for ordinary full sentences, use the article when you mean a specific bowl.

A rough pronunciation guide is:

• az ≈ awz
• itatótál ≈ ee-taw-TOH-taal
• tele ≈ TEH-leh
• van ≈ vawn

A few helpful points:

• Hungarian stress is almost always on the first syllable: ITAtótál, TELe
• á is a long vowel, roughly like a longer a
• ó is also long
• every written vowel is pronounced clearly

So the whole sentence is pronounced with clear first-syllable stress in each word:

• AZ ITAtótál TELe van.

Normally no. That is not the standard way to say it.

The natural full sentence is:

• Az itatótál tele van.

Or, with emphasis:

• Tele van az itatótál.

But Tele az itatótál is incomplete because van is missing. In present tense, Hungarian often omits van in some sentences with third-person subjects, but not in this tele van expression. So you should keep van here.

Most often, itatótál suggests a bowl used for drinking water, especially for animals.

So in context it could mean:

• a pet’s water bowl
• a livestock drinking bowl
• some other container meant for drinking water

If you just want to say bowl in a more general sense, Hungarian often uses tál. But itatótál is more specific: a bowl for drinking/watering.