Egyáltalán nincs időm.

Egyáltalán adds emphasis. In this sentence, it means something like at all, absolutely, or in any way.

So:

• Nincs időm. = I have no time.
• Egyáltalán nincs időm. = I have absolutely no time / no time at all.

It makes the statement stronger.

In Hungarian, the verb van (to be) has a special negative form in the 3rd person:

• van = is / there is
• nincs = is not / there isn't

So Hungarian says:

• Van időm. = I have time.
• Nincs időm. = I don't have time.

You do not normally say nem van in standard Hungarian for this meaning.

This is one of those forms you simply have to learn as a unit:

• van → nincs when negated in this kind of sentence

Hungarian usually does not use a verb meaning to have in basic possession sentences the way English does.

Instead, it uses a structure that is closer to:

• there is my time
• there isn't my time

So:

• Van időm. literally: There is my time
• Nincs időm. literally: There isn't my time

Natural English translates this as I have time / I don't have time.

This is a very common Hungarian pattern:

• Van pénzem. = I have money.
• Nincs testvérem. = I don't have a sibling.
• Van egy autóm. = I have a car.

The -m ending means my.

So:

• idő = time
• időm = my time

Hungarian often shows possession with an ending on the noun instead of a separate word like my.

A few examples:

• könyv = book

• könyvem = my book

• ház = house

• házam = my house

• idő = time
• időm = my time

In this sentence, időm is what allows the meaning I have time / I have no time.

There is no separate I here, because Hungarian does not need it.

The idea of my is already built into időm, and that is enough to show whose time we are talking about. So I is understood from the possession.

You could add nekem or én in some contexts for contrast or emphasis, but in a normal sentence it is unnecessary:

• Nincs időm. = I don't have time.
• Nekem nincs időm. = I don't have time (with extra emphasis, contrast, or topic marking)

So the sentence is complete without a separate pronoun.

Not in the way an English speaker might expect.

In Egyáltalán nincs időm, the important thing is that Hungarian is using an existential possession structure, not a normal I have verb form.

The possessed noun is időm (my time), and nincs is the negative existential form meaning there is not.

So the sentence is structured more like:

• At all there-is-not my-time

That is why you do not get a special 1st-person verb form here.

The word order is natural, but not completely fixed.

Egyáltalán often comes before the part it emphasizes. Here it emphasizes the negation strongly:

• Egyáltalán nincs időm.

This sounds very natural and means I have absolutely no time.

You may also hear:

• Nincs egyáltalán időm.

This is also understandable, but Egyáltalán nincs időm is a very common and smooth way to say it.

Hungarian word order often reflects focus, emphasis, and information structure, not just grammar.

Yes. That is a very common sentence.

• Nincs időm. = I have no time / I don't have time.
• Egyáltalán nincs időm. = I have absolutely no time / no time at all.

So egyáltalán is optional. It makes the sentence stronger and more emphatic.

A rough pronunciation guide:

• egyáltalán ≈ edgy-aal-ta-laan
• nincs ≈ neench
• időm ≈ ee-durm or ee-duhm depending on how detailed you want to be

A few useful notes:

• gy is a soft consonant, somewhat like the d in British duke or a softened dy sound.
• cs sounds like ch in church.
• ő is a long front rounded vowel. English does not have it exactly.
• Stress in Hungarian is always on the first syllable of the word:
  • EGYáltalán
  • NINCS
  • Időm

The positive counterpart is van.

Compare:

• Van időm. = I have time.
• Nincs időm. = I have no time.

So when learning vocabulary, it helps to remember this pair:

• van = is / there is
• nincs = is not / there isn't

They function together very often in Hungarian.

No, not for the normal meaning.

Nincs is already negative, so adding nem would be wrong in an ordinary sentence.

Use:

• Nincs időm.
• Egyáltalán nincs időm.

not:

• Nem nincs időm.

As a general rule, once you use nincs, the negation is already there.

No. Időm does not need an article in this sentence.

Hungarian does not use articles in exactly the same way English does, and possessed nouns often appear without one in sentences like this:

• Van pénzem. = I have money.
• Van időm. = I have time.
• Nincs kedvem. = I don't feel like it / I have no desire.

So időm by itself is perfectly normal here.

Yes, very many. This is a basic and useful Hungarian pattern.

Examples:

• Van időm. = I have time.
• Nincs pénzem. = I have no money.
• Van egy testvérem. = I have a sibling.
• Nincs autóm. = I don't have a car.
• Egyáltalán nincs kedvem. = I don't feel like it at all.

So if you understand Egyáltalán nincs időm, you are learning a very important Hungarian structure.