A beringela fica muito boa com tomate.

Because beringela is a feminine noun in Portuguese, so it takes the feminine singular article a.

• a beringela = the aubergine / eggplant
• uma beringela = an aubergine / eggplant

As with many nouns, the gender is something you learn together with the word.

Here fica does not mean only stays or remains. In food contexts, ficar is very commonly used to mean something like:

• turns out
• works
• goes well
• ends up tasting

So A beringela fica muito boa com tomate means that aubergine goes very well with tomato or tastes very good with tomato.

This is a very natural use of ficar in Portuguese.

Because boa agrees with beringela, which is feminine singular.

• beringela → feminine singular
• so the adjective must also be feminine singular → boa

Compare:

• O tomate fica muito bom.
• A beringela fica muito boa.

Because here muito is an adverb, modifying the adjective boa. As an adverb, muito does not change form.

So:

• muito boa = very good

But when muito is an adjective or determiner meaning much/many/a lot of, it does agree:

• muita beringela = a lot of aubergine
• muitas beringelas = many aubergines

So in your sentence:

• muito = very
• boa = good

In Portuguese, when talking about ingredients or foods in a general sense, it is very common to omit the article after com.

So:

• com tomate = with tomato, with tomatoes, with tomato as an ingredient

If you say com o tomate, that usually sounds more specific, as if you mean a particular tomato or a specific tomato element already known from context.

So com tomate is the natural generic phrasing here.

Yes, you could, but it is not exactly the same.

• é muito boa com tomate = it is very good with tomato
• fica muito boa com tomate = it turns out / works / tastes very good with tomato

With food, ficar often sounds more idiomatic when talking about how ingredients combine or how a dish turns out. Ser is possible, but ficar often feels more natural in this type of sentence.

Yes. In European Portuguese, the usual word is beringela.

In Brazilian Portuguese, you will often see berinjela instead.

So for Portugal:

• beringela is the standard word

It can do both, depending on context. In this sentence, A beringela is most naturally understood as a generic statement about aubergine as a food.

Portuguese often uses the definite article to talk about things in general:

• A beringela = aubergine / eggplant, as a category
• O tomate = tomato, as a category

So even though the sentence literally starts with the aubergine, the meaning is more like aubergine in general.

This is the normal word order in Portuguese:

• verb: fica
• adverb: muito
• adjective: boa
• complement: com tomate

So the structure is basically:

• subject + verb + degree word + adjective + complement

You could move things around in some contexts, but this is the most straightforward and natural order.

Often yes, in practical meaning. Portuguese singular food nouns are frequently used in a broad ingredient sense.

So com tomate may correspond to:

• with tomato
• with tomatoes
• with tomato sauce
• with tomato as an ingredient

The exact interpretation depends on context, but the Portuguese wording is completely natural.

A broad European Portuguese pronunciation would be roughly:

• A → a short unstressed uh
• beringela → something like buh-ring-ZHEH-luh
• fica → FEE-kuh
• muito → in European Portuguese often closer to MWEE-tu
• boa → BOH-uh
• com tomate → kong tuh-MAH-tuh with reduced unstressed vowels

A very rough full approximation is:

uh buh-ring-ZHEH-luh FEE-kuh MWEE-tu BOH-uh kong tuh-MAH-tuh

European Portuguese reduces unstressed vowels a lot more than English speakers often expect.

It can do either, depending on context.

It may mean:

• aubergine as an ingredient goes well with tomato
• a particular aubergine dish turns out very well with tomato

That is one reason ficar is useful here: it works well both for general food pairings and for how something turns out when prepared.