Moja córka umie już czytać po polsku.

Because córka is a feminine noun, so the possessive adjective my must also be in the feminine form.

• mój = my (masculine singular)
• moja = my (feminine singular)
• moje = my (neuter singular)

So:

• moja córka = my daughter
• mój syn = my son
• moje dziecko = my child

Polish adjectives and possessive words must agree with the noun in gender, number, and case.

It is in the nominative singular.

That is because córka is the subject of the sentence — the person doing the action of being able to read.

You can think of the structure as:

• Moja córka = subject
• umie = knows how / can
• już = already
• czytać = to read
• po polsku = in Polish

So córka stays in its basic dictionary form here.

Yes — Polish has several ways to express ability, and they are not always interchangeable.

In this sentence, umie czytać is very natural because umieć often means to know how to do something, especially a learned skill.

• umie czytać = knows how to read / can read
• potrafi czytać = is able to read / can read
• może czytać = can read, but often means is allowed to read or it is possible for her to read

So:

• umieć = learned ability, knowing how
• potrafić = ability, often similar to be able to
• móc = can / may, often possibility or permission

For a child learning a language, umie już czytać po polsku sounds very natural.

Because after umieć you normally use the infinitive of the action.

So the pattern is:

• umie + infinitive

Examples:

• Umiem pływać = I can swim / I know how to swim
• Umie gotować = He/she can cook
• Moja córka umie czytać = My daughter can read

This is similar to English can read, except Polish uses a full verb meaning know how to plus the infinitive.

Już means already.

It shows that something has happened sooner than expected or that a new stage has been reached.

So Moja córka umie już czytać po polsku suggests something like:

• she has reached that ability now
• perhaps surprisingly early
• or earlier than before

Without już:

• Moja córka umie czytać po polsku = My daughter can read in Polish

With już:

• Moja córka umie już czytać po polsku = My daughter can already read in Polish

Because po polsku is the standard Polish expression for in Polish when talking about language.

This pattern is very common:

• po polsku = in Polish
• po angielsku = in English
• po niemiecku = in German
• po hiszpańsku = in Spanish

So when you talk about speaking, reading, writing, or saying something in a language, po + language adverb form is usually what you want.

Examples:

• Mówię po polsku = I speak Polish / in Polish
• Pisze po angielsku = He/she writes in English
• Czyta po francusku = He/she reads in French

Polsku is part of the fixed expression po polsku.

Historically and grammatically, it comes from an adjectival form used after po, and for learners it is best to remember it as a set phrase meaning in Polish.

You do not normally build it freely the way you might in English. It is better to learn these as chunks:

• po polsku
• po angielsku
• po rosyjsku
• po włosku

That will sound much more natural than trying to translate word-for-word from English.

Yes, Polish word order is fairly flexible, and już can move depending on emphasis.

The neutral version here is:

• Moja córka umie już czytać po polsku.

You may also hear:

• Moja córka już umie czytać po polsku.
• Już moja córka umie czytać po polsku. (more marked, special emphasis)
• Moja córka umie czytać już po polsku. (possible, but less neutral)

The most natural placements are usually either:

• już umie
• umie już czytać

The exact nuance depends on what the speaker wants to highlight.

Yes, that is grammatically correct and natural.

The difference is slight:

• umie czytać stresses that she has learned the skill
• potrafi czytać stresses ability/capability

In many everyday contexts, both work.

Still, for things like reading, writing, swimming, cooking, and speaking a language, umieć is especially common because it strongly suggests knowing how.

Yes — only czytać po polsku works for the meaning read in Polish.

• czytać po polsku = read in Polish
• czytać po polskie = incorrect
• czytać polski = incorrect for this meaning

If you want to say read Polish in the sense of read the Polish language, Polish still typically says:

• czytać po polsku

If you want to say read a Polish text/book/newspaper, then the adjective agrees with the noun:

• czytać polską książkę = read a Polish book
• czytać polską gazetę = read a Polish newspaper
• czytać polskie teksty = read Polish texts

A rough pronunciation guide:

• córka ≈ TSOOR-ka
• czytać ≈ CHI-tach (very rough English approximation)

A few important points:

• ó sounds like u
• cz sounds like English ch
• y is a hard central vowel; there is no exact English equivalent
• final ć is a soft ch-like sound
• rz is not in this sentence, but learners often confuse Polish consonant spellings, so it is worth staying alert

More carefully:

• córka = [TSOOR-ka]
• czytać = [CHI-tach’] with a soft final consonant

If you want to sound more natural, pay attention to stress too: Polish usually stresses the second-to-last syllable.

• MO-ja
• CÓR-ka
• U-mie
• CZY-tać
• POL-sku

Because Polish often does not need subject pronouns when the subject is already clear.

Here the subject is explicitly given as moja córka, so there is no need to add ona.

In fact, adding ona would usually sound unnecessary unless you want extra emphasis or contrast.

Compare:

• Moja córka umie już czytać po polsku. = neutral
• Ona umie już czytać po polsku. = She can already read in Polish
• Moja córka, ona już umie czytać po polsku. = possible, but emphatic or contrastive

Polish commonly leaves pronouns out unless they are needed for emphasis, contrast, or clarity.

In practice, the intended meaning is read in Polish or read Polish-language text.

Because of po polsku, the focus is on the language used.

So the sentence naturally means that your daughter has acquired the ability to read texts written in Polish.

If you remove po polsku, then:

• Moja córka umie już czytać = My daughter can already read

Adding po polsku specifies the language in which she can read.

Yes, very normal.

It sounds natural, idiomatic, and conversational. A Polish speaker could easily say this when talking about a child learning to read or learning Polish.

Possible close variants include:

• Moja córka już umie czytać po polsku.
• Córka umie już czytać po polsku.
• Moja córka potrafi już czytać po polsku.

But the original sentence is perfectly good standard Polish.