El ruido constante puede causar dolor de cabeza.

Because constante is an adjective ending in -e, and adjectives of that type usually do not change for masculine and feminine.

So you get:

• ruido constante
• música constante

It only changes for number:

• ruidos constantes
• molestias constantes

Puede is the third-person singular form of poder and causar is an infinitive. The pattern poder + infinitive means can / may / is able to do something.

So:

• puede causar = can cause / may cause

Because the subject is singular: el ruido constante. A singular subject takes a singular verb.

Compare:

• El ruido constante puede causar...
• Los ruidos constantes pueden causar...

Spanish often leaves out the article with illnesses or symptoms when speaking in a general way, especially after verbs like causar, tener, or provocar.

So causar dolor de cabeza is very natural.

If you said causar un dolor de cabeza, it would sound more like causing one specific headache or would give the phrase more emphasis.

Yes. Dolor de cabeza is the standard expression for headache. Literally, it is pain of the head, but it is best learned as a whole chunk.

Spanish uses the same pattern in many similar expressions:

• dolor de espalda = back pain
• dolor de muelas = toothache
• dolor de garganta = sore throat

For the medical symptom headache, Spanish normally uses the fixed expression dolor de cabeza.

Dolor en la cabeza is possible, but it sounds more literal, as if you are simply describing pain located in the head. If you mean the common condition a headache, dolor de cabeza is the usual choice.

Because ruido usually means noise, especially something unpleasant, distracting, or unwanted. Sonido is more neutral and simply means sound.

Since the sentence is about something that can lead to a headache, ruido fits much better than sonido.

Yes. A few common alternatives are:

• provocar — similar to causar, slightly more formal or technical in some contexts
• dar — very common in everyday speech

Examples:

• El ruido constante puede provocar dolor de cabeza.
• El ruido constante da dolor de cabeza.

All are possible, but causar works very well in a neutral, informative sentence.

In standard Spain Spanish, the z in cabeza is pronounced like the th in think.

So roughly:

• cabeza ≈ ka-BE-tha
• ruido ≈ RWEE-do
• puede ≈ PWE-de
• causar ≈ kau-SAR

Also, in ruido, the r is a soft single r, not the strong rolled rr sound.