Я не хочу пропустить завтрак.

Хочу is the 1st person singular present-tense form of хотеть (to want).

So:

• я хочу = I want
• я не хочу = I do not want / I don't want

Even though English often says I don't want to miss..., Russian uses the present-tense form хочу in the same way.

After хотеть (to want), Russian usually uses an infinitive to say what someone wants to do.

So the structure is:

• хочу + infinitive = want to + verb

In this sentence:

• не хочу пропустить = don't want to miss

This is very common in Russian:

• Я хочу спать. = I want to sleep.
• Я хочу поесть. = I want to eat.

This is about aspect.

• пропустить = perfective
• пропускать = imperfective

Russian often uses the perfective infinitive after хочу / не хочу when talking about a single completed event.

Here, пропустить завтрак means to miss breakfast as one whole event.
So Я не хочу пропустить завтрак means I don't want to end up missing breakfast.

If you said Я не хочу пропускать завтрак, that would usually sound more like:

• I don't want to be missing breakfast
• I don't want to skip breakfast (as a habit / repeatedly)

So:

• не хочу пропустить завтрак = one specific breakfast
• не хочу пропускать завтрак = breakfast in general / as a repeated action

Завтрак is in the accusative case, because it is the direct object of пропустить.

You are missing what?
→ завтрак

For masculine inanimate nouns, the accusative singular is usually the same as the nominative singular.

So:

• nominative: завтрак
• accusative: завтрак

That is why the form does not change.

Russian has no articles. There is no direct equivalent of a/an/the.

So завтрак can mean:

• breakfast
• the breakfast
• a breakfast

The exact meaning depends on context.

In this sentence, English naturally translates it as breakfast without needing an article in most cases anyway:
I don't want to miss breakfast.

Grammatically, не goes with хочу:

• не хочу = do not want

So the basic meaning is:

• I do not want [to miss breakfast]

This is different from saying something like I want not to miss breakfast in English, even though the overall meaning is very similar.

Russian normally expresses this idea with:

• Я не хочу пропустить завтрак.

So the negation is attached to the wanting, not directly to the infinitive.

Yes. Russian word order is more flexible than English word order.

The neutral, standard order here is:

• Я не хочу пропустить завтрак.

But other orders are possible for emphasis, for example:

• Завтрак я не хочу пропустить.
  = Breakfast, I don't want to miss.

• Я завтрак не хочу пропустить.
  This can also work, depending on emphasis.

Even when the order changes, the case endings help show the grammatical role of each word.

Yes, it is very natural.

Пропустить can mean:

• to miss
• to skip
• to let pass
• to fail to attend / fail to catch, depending on context

So пропустить завтрак is a normal way to say:

• miss breakfast
• skip breakfast

The exact English translation depends on context. In many situations, skip breakfast may sound especially natural.

Then the imperfective verb would often be better:

• Я не хочу пропускать завтрак.

This means something like:

• I don't want to skip breakfast.
• I don't want to keep missing breakfast.
• I don't want to make a habit of missing breakfast.

Compare:

• Я не хочу пропустить завтрак.
  = I don't want to miss this breakfast / one specific breakfast.

• Я не хочу пропускать завтрак.
  = I don't want to skip breakfast in general.

The stress is:

• Я не хочу́ пропусти́ть за́втрак.

A rough pronunciation guide:

• ya nee kha-CHOO pruh-poos-TEET ZAAV-trak

A few notes:

• х sounds like the ch in Scottish loch or German Bach
• я = ya
• ю in хочу gives a yoo-like sound
• stressed syllables are important in Russian, so try to notice:
  • хочу́
  • пропусти́ть
  • за́втрак

Not really. Пропустить завтрак means to miss / skip breakfast, not specifically to be late.

If you want to say I don't want to be late for breakfast, Russian would use a different idea, such as:

• Я не хочу опоздать на завтрак.

So:

• пропустить завтрак = miss/skip breakfast
• опоздать на завтрак = be late for breakfast