Me duele la cabeza cuando hay mucho ruido.

Because doler works like gustar in this kind of sentence.

In Me duele la cabeza, the thing that hurts is la cabeza, so la cabeza is the grammatical subject.
Me means to me.

A very literal way to think of it is:

• Me duele la cabeza = The head hurts to me

More natural English is, of course, My head hurts or I have a headache.

So:

• me = to me
• duele = hurts
• la cabeza = the head

You do not usually say yo duelo for this meaning.

Because the verb agrees with la cabeza, which is singular.

• la cabeza → singular → duele
• las piernas → plural → duelen

Compare:

• Me duele la cabeza. = My head hurts.
• Me duelen las piernas. = My legs hurt.

So the verb matches the thing causing pain, not the person.

With body parts, Spanish often uses:

• an indirect object pronoun (me, te, le, nos, os, les)
• plus the definite article (el, la, los, las)

So Spanish prefers:

• Me duele la cabeza instead of
• Me duele mi cabeza

This is very common and natural in Spanish.

Using mi cabeza is possible in special cases, for example if you want emphasis or contrast, but in normal speech la cabeza is what you usually want.

Hay means there is or there are.

So:

• hay mucho ruido = there is a lot of noise

It comes from the verb haber.

A useful point: hay is used for both singular and plural ideas in the present:

• Hay un problema. = There is a problem.
• Hay muchos problemas. = There are many problems.

In your sentence, hay mucho ruido means that a lot of noise exists in that situation.

Because mucho is used with nouns, while muy is used with adjectives and adverbs.

Here, ruido is a noun:

• mucho ruido = a lot of noise

Compare:

• mucho ruido = a lot of noise
• muy ruidoso = very noisy

So:

• hay mucho ruido ✅
• hay muy ruido ❌

Because ruido is often treated as an uncountable noun, like noise in English.

So Spanish says:

• mucho ruido = a lot of noise

not usually

• muchos ruidos

You can say muchos ruidos if you mean many different noises/sounds, but in a general sentence like this, mucho ruido is the normal choice.

Because this sentence describes a general/habitual situation:

• My head hurts when there is a lot of noise

It is not talking about one specific future event. It means this happens in general.

So Spanish uses the present tense in both parts:

• Me duele la cabeza
• cuando hay mucho ruido

This is very natural for repeated or general truths.

Yes. That is completely correct.

Both word orders are natural:

• Me duele la cabeza cuando hay mucho ruido.
• Cuando hay mucho ruido, me duele la cabeza.

The meaning is basically the same. The difference is mainly emphasis:

• starting with Me duele la cabeza... puts the focus first on the pain
• starting with Cuando hay mucho ruido... puts the focus first on the situation

Yes, but it is a little different in tone.

• Me duele la cabeza = My head hurts
• Tengo dolor de cabeza = I have a headache

Both are correct, but me duele la cabeza is very common and often feels more direct and natural when describing the pain itself.

If you want the most natural match for the original sentence, Me duele la cabeza cuando hay mucho ruido is excellent.

Me is an indirect object pronoun.

In this sentence, it tells you who is affected by the pain:

• me = to me

Other forms are:

• me = to me
• te = to you
• le = to him/her/you (formal)
• nos = to us
• os = to you all (used in Spain)
• les = to them/you all

For example:

• Me duele la cabeza. = My head hurts.
• Te duele la cabeza. = Your head hurts.
• Nos duele la cabeza. = Our head hurts / We have a headache.

In standard Spain Spanish, cabeza is pronounced roughly like:

• ka-BEH-tha

The z in most of Spain sounds like the th in think.

So:

• cabeza → ka-BEH-tha
• duele → roughly DWEH-leh
• ruido → roughly RRWEE-doh

If you are learning Spanish from Spain, that z = th sound is worth noticing.

It is neutral and natural. You can use it in both everyday conversation and normal writing.

Nothing in the sentence is especially formal or especially casual. It is just standard Spanish.

If you want to make it sound a little more conversational, the same sentence still works perfectly:

• Me duele la cabeza cuando hay mucho ruido.

That is something a native speaker could easily say in real life.

Yes, depending on the meaning.

In your sentence, cuando hay mucho ruido describes something habitual, so the present is correct.

But with other meanings, cuando can be followed by other tenses. For example:

• Cuando había mucho ruido, me dolía la cabeza.
  = When there was a lot of noise / Whenever there was a lot of noise, my head hurt.

• Cuando haya mucho ruido, me dolerá la cabeza.
  = When there is a lot of noise / Whenever there will be a lot of noise, my head will hurt.

So the tense after cuando depends on whether you are talking about a general present situation, the past, or the future.