Budżet domowy pokazuje dochód i każdy wydatek.

Both are possible.

• budżet domowy is a very common, neutral collocation meaning household budget / home budget
• domowy budżet is also understandable and natural, but it can sound a little more descriptive or stylistically different

In Polish, adjective position is more flexible than in English. Some noun + adjective combinations become standard set phrases, and budżet domowy is one of them.

Because it has to agree with budżet.

Budżet is:

• singular
• masculine
• nominative

So the adjective also takes the matching form:

• domowy = masculine singular nominative

This is normal in Polish: adjectives change their endings to match the noun in gender, number, and case.

Pokazuje is:

• 3rd person singular
• present tense
• from the verb pokazywać = to show

So literally it means:

• it shows
• or sometimes is showing, depending on context

Here it agrees with budżet domowy, which is singular:

• Budżet domowy pokazuje... = The household budget shows...

They are the direct objects of the verb, so they are in the accusative case.

But here is the important part: both dochód and wydatek are masculine inanimate singular nouns, and in Polish that often means:

• nominative = accusative

So:

• dochód stays dochód
• wydatek stays wydatek

Even though the case has changed, the form looks the same.

Because wydatek is a masculine singular noun.

So the word każdy has to match it:

• każdy = masculine singular
• każde = neuter singular
• każda = feminine singular

That is why:

• każdy wydatek = every expense

This works just like adjective agreement in Polish.

Because każdy means each / every, and in Polish it normally goes with a singular noun.

So:

• każdy wydatek = every expense / each expense

This is similar to English:

• we say every expense, not every expenses

They are similar, but not identical.

• każdy wydatek = every single expense, one by one
• wszystkie wydatki = all expenses, as a group

So the original sentence emphasizes that the budget shows each individual expense, not just expenses in general.

Yes. That would also be natural.

The difference is:

• dochód i każdy wydatek = income and every expense
• dochody i wydatki = income(s) and expenses

The plural version sounds more general and category-based.
The original sentence sounds a bit more like the budget includes every single expense entry.

No, Polish word order is fairly flexible.

The given order:

• Budżet domowy pokazuje dochód i każdy wydatek

is neutral and natural.

You can change the order for emphasis, but then the focus changes. For example:

• Dochód i każdy wydatek pokazuje budżet domowy
  This sounds more marked and emphasizes dochód i każdy wydatek.

For learners, the original order is the safest and most natural choice.

Because Polish does not have articles like English.

So budżet domowy can mean:

• a household budget
• the household budget

The exact meaning depends on context.

This is very normal in Polish, and learners usually have to get used to understanding definiteness from the situation rather than from a separate word.

A rough pronunciation guide:

• Budżet domowy → BOO-jet do-MO-vih
• pokazuje → po-ka-ZOO-yeh
• dochód → DO-hoot
  (the ch is like the ch in Scottish loch, not like English ch in chair)
• i → ee
• każdy → KAZH-dih
• wydatek → vih-DA-tek

A few useful sound notes:

• dż in budżet sounds like English j in jam
• ż in każdy sounds like the s in measure
• ó sounds like u
• Polish stress is usually on the second-to-last syllable, so:
  • do-MO-vy
  • po-ka-ZU-je
  • wy-DA-tek

In this sentence:

• dochód = income
• wydatek = expense / expenditure

A useful distinction:

• dochód is money coming in
• wydatek is money going out

So they are a natural pair in financial language.

Yes.

Literally, pokazuje means shows. But in a sentence about a budget, English might naturally say:

• shows
• displays
• lists
• includes

depending on context.

So the Polish verb is straightforward, but the best English translation can vary a little depending on how the budget is being described.