Minha filha gosta de comer ovo no café da manhã.

Because minha has to agree with filha, the thing being possessed, not with the speaker.

• filha = daughter, a feminine singular noun
• so the possessive must also be feminine singular: minha

Compare:

• minha filha = my daughter
• meu filho = my son

This is a very common pattern in Portuguese.

Because the subject is minha filha, which is third person singular: she / my daughter.

The verb gostar is conjugated like this in the present tense:

• eu gosto = I like
• você / ele / ela gosta = you / he / she likes
• nós gostamos = we like
• vocês / eles / elas gostam = you all / they like

So:

• Minha filha gosta = My daughter likes

Because gostar normally requires the preposition de.

So you say:

• gostar de algo = to like something
• gostar de fazer algo = to like doing something / to like to do something

Examples:

• Ela gosta de música. = She likes music.
• Ela gosta de cozinhar. = She likes cooking.
• Minha filha gosta de comer ovo. = My daughter likes to eat egg/eggs.

So gosta comer would be incorrect.

After gostar de, Portuguese uses the infinitive when the next idea is an action.

• gosta de comer = likes to eat / likes eating
• gosta de estudar = likes to study / likes studying
• gosta de nadar = likes to swim / likes swimming

So comer stays in its base form because it is not the main conjugated verb. The main conjugated verb is gosta.

Also, you could shorten the idea and say:

• Minha filha gosta de ovo no café da manhã.

That means something like My daughter likes eggs/egg for breakfast, while gosta de comer ovo emphasizes the action of eating a little more.

Yes, ovos is also possible.

In Portuguese, especially with foods, the singular is often used in a general sense:

• comer ovo
• comer pão
• beber café

So comer ovo can mean to eat egg/eggs as a food in general.

If you say comer ovos, that also sounds natural and may feel a bit more concrete, like actual eggs on the plate.

So both of these are possible:

• Minha filha gosta de comer ovo no café da manhã.
• Minha filha gosta de comer ovos no café da manhã.

No is a contraction of:

• em + o = no

Here it appears in:

• no café da manhã

It means at breakfast or for breakfast, depending on how you translate it in English.

Similar contractions:

• na = em + a
• nos = em + os
• nas = em + as

Examples:

• no almoço = at lunch
• na escola = at school

Café da manhã is the normal Portuguese expression for breakfast.

Literally, it comes from:

• café = coffee
• da = de + a = of the
• manhã = morning

So literally it looks like coffee of the morning, but as a whole it simply means breakfast.

This is a fixed expression, so learners should treat café da manhã as one vocabulary item.

In Brazilian Portuguese, the definite article before a possessive is often optional.

So both can be correct:

• minha filha
• a minha filha

In everyday Brazilian Portuguese, especially before family words, leaving out the article is very common and natural.

Very roughly:

• minha filha = very common, natural
• a minha filha = also correct, sometimes a little more explicit or regionally preferred

So the sentence sounds perfectly normal without the article.

The tricky part is lh.

• filha is pronounced approximately FEE-lya

The lh sound is similar to the lli sound in some pronunciations of million, though it is not exactly the same in every accent.

A rough breakdown:

• fi = fee
• lha = lya

So: FEE-lya

The tricky part here is nh and the final nasal sound.

A rough pronunciation is:

• manhã ≈ ma-NYÃ

Notes:

• nh sounds like ny in canyon
• the final ã is nasal, so it is not a plain ah

So café da manhã sounds roughly like:

• ka-FEH da ma-NYÃ

That final nasal vowel is very important in natural Brazilian Portuguese pronunciation.