Mam już pokrojoną cukinię i przygotowaną fasolę do zupy.

Because they are feminine singular direct objects of mam (I have), so they appear in the accusative case.

• cukinia → cukinię
• fasola → fasolę

This is a very common pattern for feminine nouns ending in -a:

• nominative: zupa
• accusative: zupę

So in this sentence, mam requires the thing possessed to be in the accusative:

• Mam cukinię
• Mam fasolę

Because they agree with the nouns they describe.

Both pokrojoną and przygotowaną describe feminine singular nouns in the accusative:

• pokrojoną describes cukinię
• przygotowaną describes fasolę

So the pattern is:

• pokrojona cukinia → nominative
• pokrojoną cukinię → accusative

and

• przygotowana fasola → nominative
• przygotowaną fasolę → accusative

In other words, the adjective/participle has to match the noun in gender, number, and case.

They are best understood as adjectival participles—forms that come from verbs but behave like adjectives.

• pokrojona comes from pokroić (to cut up, slice)
• przygotowana comes from przygotować (to prepare)

They function like adjectives meaning:

• pokrojona cukinia = sliced zucchini
• przygotowana fasola = prepared beans / prepared bean mixture

So although they come from verbs, in this sentence they act like descriptive words attached to nouns.

Because Polish often uses mieć + object + participle/adjective to emphasize the current state/result.

So:

• Mam pokrojoną cukinię focuses on the fact that the zucchini is already sliced now
• Pokroiłem / Pokroiłam cukinię focuses more on the action I sliced the zucchini

The sentence with mam is very natural when you want to say that something is already done and ready.

Już means already.

In this sentence:

• Mam już pokrojoną cukinię... = I already have sliced zucchini...

Its placement is flexible, but it often appears early in the sentence, usually after the verb or near the word it emphasizes.

Common possibilities:

• Już mam pokrojoną cukinię.
• Mam już pokrojoną cukinię.

Both are natural, though the emphasis can shift slightly.

Here do zupy means for the soup.

The preposition do often means for, to, or into, depending on context. In cooking, do zupy very often means something like:

• for soup
• to use in soup

So this sentence means that the zucchini and beans are prepared as ingredients intended for soup.

If you wanted to emphasize physical movement into the soup, Polish would more naturally use a different structure depending on the context.

Grammatically, it sits closest to fasolę, so at first glance it may seem to attach only to that noun. But in natural context, many speakers will understand it as referring to the overall food preparation, often effectively to the whole list of ingredients.

So the sentence is naturally understood as something like:

• I already have sliced zucchini and prepared beans for the soup.

If you want to make it completely clear that both are for the soup, you could rephrase:

• Mam już pokrojoną cukinię i przygotowaną fasolę na zupę.
• Mam już do zupy pokrojoną cukinię i przygotowaną fasolę.

The original sentence is still normal and understandable.

Because in Polish fasola can function as a mass/collective ingredient noun, not only as a countable singular noun meaning a bean plant or a type of bean.

In cooking, Polish often uses singular ingredient nouns where English may prefer a plural:

• fasola = beans
• marchew = carrot as an ingredient
• cebula = onion as an ingredient

So przygotowaną fasolę can naturally mean prepared beans as a food ingredient.

Because the speaker is talking about the ingredients as singular food items/substances, not as multiple separate countable units.

• cukinia often works like zucchini/courgette as an ingredient
• fasola often works like beans as a food mass/ingredient

Using the singular is very natural in recipe or kitchen context.

Plural forms would change the meaning slightly and make it sound more like separate individual items or types:

• cukinie = multiple zucchinis
• fasole = multiple kinds/batches of beans, less common in ordinary kitchen talk

Yes. Polish word order is fairly flexible, because case endings show grammatical relationships.

The original:

• Mam już pokrojoną cukinię i przygotowaną fasolę do zupy.

Other possible variants:

• Już mam pokrojoną cukinię i przygotowaną fasolę do zupy.
• Pokrojoną cukinię i przygotowaną fasolę do zupy mam już.

But the original order is the most neutral and natural in everyday speech.

Word order changes usually affect emphasis, not the core meaning.

Yes, very often.

It comes from pokroić and means something like:

• cut up
• sliced
• chopped

The exact English translation depends on context.

For example:

• pokrojona cebula = chopped/sliced onion
• pokrojony chleb = sliced bread
• pokrojone warzywa = chopped/cut-up vegetables

So pokrojona cukinia is very natural kitchen language.

It is understandable, but in natural English you would usually say something more like:

• I already have the zucchini sliced and the beans prepared for the soup.
• I already have sliced zucchini and prepared beans for the soup.

That is because the Polish structure mam + noun + participle often corresponds to English have something done/ready or to a more natural adjective-based phrase.

So a literal word-for-word translation is useful for grammar, but not always the best final English version.