Minha irmã gosta de fazer ovos com tomate.

Because irmã is a feminine noun, so the possessive has to match it:

• meu = my, for masculine singular nouns
• minha = my, for feminine singular nouns

So:

• meu irmão = my brother
• minha irmã = my sister

The possessive agrees with the thing possessed, not with the speaker.

Yes. In Brazilian Portuguese, it is very common to use the definite article before possessives:

• Minha irmã gosta de fazer ovos com tomate.
• A minha irmã gosta de fazer ovos com tomate.

Both are correct. In Brazil, the version with the article is often very natural in everyday speech, but leaving it out is also perfectly normal.

Because the verb gostar normally requires the preposition de.

So you say:

• gostar de + noun
  • Ela gosta de música. = She likes music.
• gostar de + infinitive
  • Ela gosta de cozinhar. = She likes to cook.

That is why:

• gosta de fazer = likes to make/do

Gostar fazer is not correct standard Portuguese.

Here fazer means to make or to prepare.

Portuguese fazer is broader than English make in some contexts. With food, it often means:

• to make
• to prepare
• sometimes, in natural English translation, to cook

So fazer ovos can mean make eggs or cook eggs, depending on context.

Because fazer is very common when talking about preparing food in general.

For example:

• fazer almoço = make lunch
• fazer café = make coffee
• fazer um bolo = make a cake
• fazer ovos = make eggs

You could use a more specific cooking verb in some situations, but fazer sounds very natural and everyday here.

Because ovos means eggs. The sentence is talking about preparing eggs as a dish, not just one egg.

• ovo = egg
• ovos = eggs

In cooking, the plural is very common because people usually prepare more than one egg, or because eggs is being used as the name of the dish.

In Portuguese, when talking about ingredients, the singular is often used in a general way.

So:

• ovos com tomate = eggs with tomato

This can mean tomato as an ingredient, not necessarily exactly one whole tomato.

You may also hear:

• ovos com tomates

That would sound more like there are noticeable pieces or multiple tomatoes involved. The singular often sounds more like a general ingredient label, similar to menu language.

Because after com, when naming ingredients or foods in a general sense, Portuguese often does not use an article.

So these are natural:

• com tomate
• com queijo
• com cebola

If you add an article, it usually sounds more specific:

• com o tomate = with the tomato

That would suggest a particular tomato already known in the conversation, not just tomato as an ingredient.

Not exactly.

• gosta de fazer ovos com tomate = she likes making/preparing eggs with tomato
• gosta de ovos com tomate = she likes eggs with tomato

The first focuses on the activity of preparing the dish.
The second focuses on liking the dish itself.

So adding fazer changes the meaning slightly.

Yes. Both are good translations.

In Portuguese, gostar de + infinitive can often be translated in English as:

• likes to make
• likes making

So:

• Minha irmã gosta de fazer ovos com tomate. = My sister likes to make eggs with tomato. = My sister likes making eggs with tomato.

Irmã has a nasal vowel at the end. The ã is not pronounced like a normal English a.

A rough guide:

• irmã sounds something like eer-MAHN or eer-MUHNG, but very lightly nasalized

Important points:

• the stress is on the last syllable: irmÃ
• the ã is nasal, meaning some air goes through the nose while saying it

English does not have this exact sound, so approximation is normal at first.

It follows a very standard Portuguese pattern:

• Minha irmã = subject
• gosta de = verb + required preposition
• fazer = infinitive
• ovos com tomate = object/complement

So the structure is:

[Subject] + [gostar de] + [infinitive] + [thing being made]

This is a very common pattern in Portuguese, for example:

• Meu pai gosta de ler livros.
• Ela gosta de cozinhar arroz.
• Nós gostamos de assistir filmes.

No. With gostar, the correct preposition is de, not em.

So:

• gostar de = correct
• gostar em = not correct in standard Portuguese for this meaning

You should learn gostar de as a fixed pattern.