Stałe wydatki, zmienne wydatki i nadwyżka są zapisane.

Because they are adjectives agreeing with wydatki.

In Polish, adjectives change their endings to match the noun in:

• gender
• number
• case

Here, wydatki is plural, and it is a non-masculine-personal plural noun, so the adjectives take the plural ending -e:

• stały wydatek = a fixed expense

• stałe wydatki = fixed expenses

• zmienny wydatek = a variable expense
• zmienne wydatki = variable expenses

So the ending -e is there because the adjectives must match wydatki.

The singular form is wydatek.

So:

• wydatek = expense
• wydatki = expenses

This is a very common Polish plural pattern where the singular and plural look quite different:

• wydatek → wydatki

A learner might expect something more regular, but this kind of change is normal in Polish.

They are in the nominative case, because they are the subject of the sentence.

The full subject is:

• Stałe wydatki
• zmienne wydatki
• i nadwyżka

Together, these are the things that are recorded / are written down, so they appear in the nominative.

That is why you see:

• wydatki (not a different case form)
• nadwyżka (basic dictionary form)

Because the subject is a list of several things, not just nadwyżka by itself.

The sentence includes:

• stałe wydatki
• zmienne wydatki
• nadwyżka

Since all of these together form a compound subject, Polish uses the plural verb:

• są = are

So even though nadwyżka is singular on its own, the whole subject is plural in meaning.

Są zapisane is a passive/resultative-style structure meaning something like:

• are written down
• are recorded
• have been entered

It describes the state/result of those items.

Breakdown:

• są = are
• zapisane = written down / recorded

So są zapisane means the expenses and surplus are already in a written/recorded state.

Compare:

• zapisują = they are writing down / they write down
  This is an active verb and would need a subject meaning they.

• zapisano = it was written down / people wrote it down
  This is impersonal and does not name the subject in the same way.

So są zapisane fits well when you want to say that these items are already recorded.

For the same reason the adjectives do: it agrees with the subject.

Zapisane is a participle used like an adjective, so it matches the nouns it describes.

The full subject is plural and non-masculine-personal, so the correct plural ending is -e:

• zapisany = singular masculine
• zapisana = singular feminine
• zapisane = singular neuter or plural non-masculine-personal

Here it is plural non-masculine-personal, so zapisane is correct.

Yes, very often you could.

A more compact version would be:

• Stałe i zmienne wydatki oraz nadwyżka są zapisane.

That means the same thing.

Why repeat wydatki in the original sentence?

• to make the structure extra clear
• to emphasize the contrast between fixed expenses and variable expenses
• because lists in Polish often repeat nouns for clarity

So both are possible, but the repeated noun is not wrong at all.

Because in Polish, just like in English, you normally do not put a comma before i when it simply means and and joins the last item in a list.

So:

• Stałe wydatki, zmienne wydatki i nadwyżka...

This is standard punctuation:

• comma between earlier items
• no comma before i

You would only use a comma before i in special cases, not in a normal simple list like this.

Yes. Polish word order is more flexible than English word order.

This sentence could be rearranged, for example:

• Stałe wydatki, zmienne wydatki i nadwyżka są zapisane.
• Są zapisane stałe wydatki, zmienne wydatki i nadwyżka.

The original version is the most neutral and natural if you are simply naming the items first and then saying what state they are in.

Changing the order usually changes:

• focus
• emphasis
• sometimes style

But it does not necessarily change the basic meaning.

A few parts may be difficult for English speakers:

• stałe ≈ STAH-weh
  The letter ł is pronounced like English w.

• zmienne ≈ ZMYEN-neh
  The zm cluster at the beginning may feel unusual.
  The ie here sounds roughly like ye.

• nadwyżka ≈ nad-VIHSH-ka
  The letter ż sounds like the s in measure.
  The y is not exactly English ee or ih; it is a central Polish vowel.

• zapisane ≈ zah-pee-SAH-neh

Also note the difference between:

• stałe with ł = fixed, constant
• stale without ł = stale

That is an important spelling and pronunciation difference.

It can mean any of those, depending on context.

The verb zapisać / zapisywać is broad. It can mean:

• to write something down
• to note something
• to record something
• to enter something, for example in a document, table, or system

So są zapisane may be understood as:

• are written down
• are recorded
• are entered

The best English choice depends on the situation:

• on paper: written down
• in a spreadsheet or form: entered
• in an accounting context: recorded

Because nouns in Polish belong to grammatical genders, and nadwyżka is a feminine noun.

A very common clue is the ending -a, which often signals feminine gender:

• nadwyżka = surplus

That matters when the noun is used with adjectives or participles in the singular:

• duża nadwyżka = a large surplus
• nadwyżka jest zapisana = the surplus is recorded

But in your sentence, the verb phrase agrees with the whole list, so you get plural są zapisane instead.