Ona bierze ołówek z pudełka.

Yes. In Polish, subject pronouns are often omitted because the verb form already shows who is doing the action.

• bierze = he/she/it takes / is taking
• So Bierze ołówek z pudełka. can already mean She is taking a pencil from the box, if the context makes it clear.

Using ona adds emphasis, contrast, or clarity. For example:

• Ona bierze ołówek, a on długopis. = She takes a pencil, and he takes a pen.

So in this sentence, ona is grammatical, but not always necessary.

Bierze is the 3rd person singular present tense form of brać, which means to take.

So:

• ja biorę = I take / am taking
• ty bierzesz = you take / are taking
• on/ona/ono bierze = he/she/it takes / is taking

In this sentence, bierze can mean either:

• takes
• is taking

Polish present tense often covers both the simple present and the present continuous that English separates.

Because brać is the dictionary form, also called the infinitive: to take.

When you conjugate it, the stem changes:

• brać → biorę, bierzesz, bierze...

This is normal in Polish. Many common verbs change internally when conjugated, so you cannot always predict the present-tense form just by removing -ć.

Yes, Polish nouns often change form depending on their role in the sentence. Here, ołówek is the direct object, so it is in the accusative case.

But for many masculine inanimate nouns, the accusative singular is the same as the nominative singular.

So:

• nominative: ołówek = pencil
• accusative: ołówek = pencil

That is why it looks unchanged.

Yes. That is a very important point.

For masculine nouns:

• masculine inanimate often has accusative = nominative
• masculine animate often has accusative = genitive

Compare:

• Widzę ołówek. = I see a pencil.
  (ołówek stays the same)
• Widzę kota. = I see a cat.
  (not kot, but kota)

So ołówek stays ołówek because it is masculine inanimate.

Because the preposition z in the meaning from / out of requires the genitive case.

The noun pudełko means box, and its genitive singular form is pudełka.

So:

• nominative: pudełko
• genitive: pudełka

That is why you get:

• z pudełka = from the box / out of the box

Here, z means from or out of.

So:

• z pudełka = from the box / out of the box

Polish z can also mean with in other contexts, but then it works differently and the meaning comes from context.

For example:

• kawa z mlekiem = coffee with milk
• bierze ołówek z pudełka = she takes a pencil from the box

So in this sentence, it clearly means movement from inside the box.

Yes, bierze is correct and natural, but Polish might also use a more specific verb depending on context.

For example:

• bierze ołówek z pudełka = she takes a pencil from the box
• wyjmuje ołówek z pudełka = she takes a pencil out of the box / removes it from the box

Wyjmuje focuses more strongly on removing something from inside something.
Bierze is more general: takes.

So your sentence is perfectly good, but wyjmuje would sound more specific.

Yes.

Polish present tense often does not distinguish between:

• a general present
• an action happening right now

So Ona bierze ołówek z pudełka can mean:

• She takes a pencil from the box
• She is taking a pencil from the box

The exact meaning depends on context.

Because Polish has no articles.

English uses:

• a pencil
• the pencil

Polish usually just says:

• ołówek

The listener understands from context whether it means:

• a pencil
• the pencil
• sometimes even one pencil

So ołówek in this sentence could be translated as a pencil or the pencil, depending on the situation.

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

The neutral order here is:

• Ona bierze ołówek z pudełka.

But other orders are possible, for example:

• Z pudełka ona bierze ołówek.
• Ołówek ona bierze z pudełka.

These alternatives may sound more marked, emphasizing a certain part of the sentence.

Roughly speaking:

• neutral statement: Ona bierze ołówek z pudełka.
• emphasis on the source: Z pudełka ona bierze ołówek.
• emphasis on the object: Ołówek ona bierze z pudełka.

So the original order is the most straightforward one for a learner.

A few useful pronunciation points:

• ł is pronounced like English w
• ó is pronounced like u
• rz in bierze sounds like zh in measure

So approximately:

• Ona ≈ OH-na
• bierze ≈ BYE-zhe or BYE-rzhe depending on how detailed you want to be
• ołówek ≈ o-WOO-vek
• z pudełka ≈ s poo-DEW-ka or z poo-DEW-ka depending on sound assimilation in connected speech

Also, Polish stress is usually on the second-to-last syllable:

• O-na
• BIE-rze
• o-ŁÓ-wek
• pu-DEŁ-ka

In actual pronunciation, Polish consonants often change their voicing depending on nearby sounds.

The preposition z is normally pronounced like a voiced z, but before a voiceless consonant it is often pronounced more like s.

Since p in pudełka is voiceless, z pudełka is often pronounced close to:

• s pudełka

This is a pronunciation rule, not a spelling change. You still write:

• z pudełka

Pudełko is neuter.

You can often recognize many neuter nouns by the ending -o or -e.

Its gender matters because Polish nouns change according to declension patterns, and neuter nouns have their own set of endings. Here that matters in the genitive singular:

• pudełko → pudełka

So yes, gender is important because it helps determine how the noun changes in different cases.