Gdy będę miała mniej pracy, zrobię zupę z fasoli, cukinii i kalafiora, a na deser podam brzoskwinie z borówkami.

Because the sentence talks about the future.

• mam = I have / I am having now
• będę miała = I will have

Also, miała shows that the speaker is female. A male speaker would say będę miał.

With the imperfective verb mieć, Polish makes the future with będę + another form:

• będę mieć
• będę miała / będę miał

All of these are future forms.

That is a major difference between English and Polish.

In Polish, if the meaning is future, it is very normal to use a future form in the gdy/kiedy clause:

• Gdy będę miała mniej pracy, ...

English usually avoids will after when, but Polish does not follow that rule. So this Polish sentence is completely natural.

In this sentence, they are very close in meaning: both can mean when.

• gdy often sounds a bit more formal, literary, or written
• kiedy is very common in everyday speech

So you could also say:

• Kiedy będę miała mniej pracy, zrobię...

One more difference: kiedy can also be a question word meaning when?, but gdy cannot.

Because mniej requires the genitive.

Here praca means work in a general, uncountable sense, so Polish uses the genitive singular:

• praca → pracy

Compare:

• mam mniej czasu = I have less time
• mam mniej pracy = I have less work
• mam mniej książek = I have fewer books

So after mniej, the noun usually changes case.

Because they are perfective verbs.

In Polish, perfective verbs do not normally have a true present tense. Their present-looking forms actually refer to the future:

• zrobię = I will make
• podam = I will serve

This is very common in Polish.

Compare:

• robię = I am making / I make

• zrobię = I will make, and the action will be completed

• podaję = I am serving / I serve
• podam = I will serve

Because zupa is the direct object of zrobię, so it must be in the accusative.

• nominative: zupa
• accusative: zupę

This is a very common feminine pattern:

• kawa → kawę
• sałata → sałatę
• zupa → zupę

So zrobię zupę means I will make soup.

Because brzoskwinie is the accusative plural, and for this type of noun it has the same form as the nominative plural.

• singular: brzoskwinia
• accusative singular: brzoskwinię
• plural: brzoskwinie
• accusative plural: brzoskwinie

So:

• podam brzoskwinię = I will serve a peach
• podam brzoskwinie = I will serve peaches

Because z can govern different cases and have different meanings.

1) z + genitive = made from / of

• zupa z fasoli, cukinii i kalafiora
• soup made from beans, zucchini, and cauliflower

That is why we get:

• fasoli
• cukinii
• kalafiora

2) z + instrumental = with / together with

• brzoskwinie z borówkami
• peaches with blueberries

That is why we get:

• borówkami (instrumental plural)

So the same preposition z can mean different things depending on the case.

Because the base form is cukinia, and in the genitive singular the ending changes in a way that produces -ii.

• nominative: cukinia
• genitive: cukinii

This happens with some nouns ending in -ia. The spelling may look unusual at first, but cukinii is the correct form here.

Because na deser means for dessert, so na is expressing purpose/function, not location.

In this use, Polish takes the accusative:

• na obiad = for lunch
• na kolację = for dinner
• na deser = for dessert

Na deserze would suggest a location-like meaning, which is not what is meant here.

Because Polish often omits subject pronouns when they are clear from the verb form.

Here the verbs already show first person singular:

• będę miała
• zrobię
• podam

So ja is unnecessary unless the speaker wants extra emphasis:

• Ja zrobię zupę = I will make the soup

Without emphasis, Polish usually just leaves the pronoun out.

Because a often introduces a new but related idea, or a small shift in topic.

Here the speaker moves from the main dish to dessert:

• first: the soup
• then: dessert

So a na deser feels like:

• and as for dessert
• and for dessert

You could sometimes use i, but a sounds very natural here because it marks that little transition.

There are two main reasons.

1) A comma after the opening gdy clause

• Gdy będę miała mniej pracy, zrobię...

In Polish, an introductory subordinate clause is separated by a comma from the main clause.

2) A comma before a

• ..., a na deser podam...

When a connects two clauses or two larger parts of a sentence, Polish normally uses a comma before it.

So the punctuation here is standard Polish punctuation.