Fa una setmana que la meva filla menja iogurt amb cereals cada matí.

This is a very common Catalan way to express duration up to the present.

• fa is the verb fer in the 3rd person singular.
• In time expressions, fa + time period + que + verb means something like it has been ... that or for ... now.

So fa una setmana que... tells you that the situation began one week ago and is still true now.

A very similar example:

• Fa dos mesos que estudio català. = I’ve been studying Catalan for two months.

Because the action is still ongoing.

In Catalan, when you use fa ... que for something that started in the past and continues into the present, the main verb is often in the present tense.

So:

• Fa una setmana que la meva filla menja...

corresponds to English forms like:

• My daughter has been eating...
• For a week now, my daughter eats...
  though in natural English, the present perfect/progressive is more common.

Catalan uses the present here where English often prefers has been eating.

Yes. That is another very common way to say almost the same thing.

You could say:

• Des de fa una setmana, la meva filla menja iogurt amb cereals cada matí.

Both fa una setmana que... and des de fa una setmana... are natural.

A rough difference:

• fa una setmana que... often feels a bit more like it’s been a week that...
• des de fa una setmana... feels more like for the last week / since a week ago

In everyday use, they are often interchangeable.

Because Catalan normally uses the definite article before possessives.

So Catalan usually says:

• la meva filla
• el meu pare
• la nostra casa

This is different from English, where you normally say my daughter, not the my daughter.

So the article here is completely normal and expected in standard Catalan.

menja is the 3rd person singular present of menjar.

The subject is la meva filla, which is singular, so the verb must also be singular:

• jo menjo
• tu menges
• ell / ella menja
• nosaltres mengem
• vosaltres mengeu
• ells / elles mengen

So la meva filla menja = my daughter eats / is eating

Because iogurt is being used in a general, non-specific sense.

Here, the sentence is talking about what she eats as part of a habit, not about one specific yogurt. Catalan often leaves out the article with food or substances in this kind of context:

• menja iogurt
• beu llet
• comprem pa

This is similar to English:

• she eats yogurt not necessarily
• she eats the yogurt

If it were specific, you could use an article:

• menja el iogurt de la nevera

amb means with, so iogurt amb cereals means yogurt together with cereals.

This is the normal way to express accompaniment or combination here.

If you used de, it would usually suggest that the yogurt is a kind of yogurt made of or flavored with cereals, which is not the intended meaning.

So:

• iogurt amb cereals = yogurt with cereals
• iogurt de... would normally describe the type or composition

cada matí means every morning.

It is an expression of frequency, telling you how often the action happens. Putting it at the end is very natural in Catalan.

This sentence could also be reordered:

• Cada matí, la meva filla menja iogurt amb cereals.
• La meva filla menja iogurt amb cereals cada matí.

Adding fa una setmana que gives the full idea that this has been her routine for a week now.

It describes a repeated habit.

The key clue is cada matí. She is not eating continuously for a whole week; instead, she has had this breakfast routine every morning for the last week.

So the structure means:

• the habit started a week ago
• the habit is still continuing now

Yes, and that is often the most natural way to understand it.

A natural English rendering would be something like:

• My daughter has been eating yogurt with cereal every morning for a week.

This is a good example of a difference between the two languages:

• Catalan: often present tense after fa ... que
• English: often present perfect or present perfect progressive

So even though the Catalan verb is present, the best English equivalent is often not a simple present.

Yes, that is also possible.

For example:

• La meva filla porta una setmana menjant iogurt amb cereals cada matí.

This also means that the habit has lasted one week up to now. It often feels a bit more explicitly like has been ... for a week.

So both are natural:

• Fa una setmana que la meva filla menja...
• La meva filla porta una setmana menjant...

The version with fa ... que is extremely common and very useful to learn.