Ta cebula jest jeszcze twarda, więc smażę ją dłużej na patelni.

Because cebula is a feminine noun in Polish, and the demonstrative this has to agree with the noun’s gender.

So:

• ten = masculine
• ta = feminine
• to = neuter

Since cebula is feminine, you say ta cebula = this onion.

Cebula is the subject of the sentence, so it stays in the nominative case.

In this sentence:

• Ta cebula jest jeszcze twarda = This onion is still hard

The onion is the thing being described, not the thing directly affected by the action.

You would use cebulę in the accusative when it is a direct object, for example:

• Kroję cebulę. = I’m cutting an onion.

So here:

• cebula = subject
• ją later in the sentence = direct object pronoun referring back to the onion

Because twarda is an adjective describing cebula, and adjectives must agree with the noun in:

• gender
• number
• case

Since cebula is:

• feminine
• singular
• nominative

the adjective must also be:

• feminine
• singular
• nominative

So:

• twardy = masculine
• twarda = feminine
• twarde = neuter

That is why you get Ta cebula jest jeszcze twarda.

Because Polish normally uses the verb być (to be) in sentences like X is Y when an adjective is the predicate.

So:

• Ta cebula jest twarda. = This onion is hard.

In very casual speech, people may sometimes drop jest, but in normal standard Polish, jest is the correct form here.

So this is not like Russian, where is is often omitted in the present tense. In Polish, with this kind of sentence, jest is usually expressed.

Here jeszcze means still.

So:

• Ta cebula jest jeszcze twarda = This onion is still hard

It suggests that the onion has not reached the desired softness yet.

Be careful: jeszcze can have other meanings in different contexts, such as:

• more
• yet
• another

But in this sentence, still is the natural meaning.

Więc means so, therefore, or that’s why. It introduces the result or consequence of the first part of the sentence.

So the logic is:

• The onion is still hard
• so I’m frying it longer

That gives:

• Ta cebula jest jeszcze twarda, więc smażę ją dłużej na patelni.

Also notice the comma before więc. In Polish, a comma is normally used before conjunctions like więc when they link clauses.

Smażę is the 1st person singular present tense form of smażyć = to fry.

So:

• smażę = I fry / I am frying

In this sentence, it means:

• I’m frying it longer

The ending -ę is a common first-person singular ending in the present tense.

Examples:

• robię = I do / I am doing
• widzę = I see
• smażę = I fry / I am frying

Because the sentence describes an ongoing action, not a completed result.

• smażyć is imperfective: it focuses on the process
• usmażyć is perfective: it focuses on completing the frying

Here the speaker means:

• I’m frying it longer
• the action is in progress

So smażę is the natural choice.

If you said usmażę, it would mean more like:

• I will fry it / I’ll get it fried completely

That does not match the situation as well.

Ją is the accusative singular feminine form of ona (she/it), used here as a direct object pronoun.

It refers back to cebulę / cebula.

So:

• smażę ją = I’m frying it

Because cebula is feminine, the pronoun has to be the feminine object form:

• ją

Compare:

• Mam książkę. Czytasz ją. = I have a book. You’re reading it.
• Mam stół. Czyścisz go. = I have a table. You’re cleaning it.

Because ją is the normal accusative direct object form, while nią is usually used in the instrumental case.

Here the onion is the thing directly being fried:

• smażę ją = I’m frying it

You use nią in different structures, for example:

• Interesuję się nią. = I’m interested in her/it.
• Jest pod nią. = It is under her/it.

So in this sentence, ją is correct because the verb smażyć takes a direct object in the accusative.

Dłużej means longer or for longer.

It is an adverb, not an adjective, because it modifies the verb smażę (I fry / I am frying), not the noun cebula.

So:

• smażę ją dłużej = I’m frying it longer / for longer

The basic adverb is:

• długo = long / for a long time

Its comparative form is:

• dłużej = longer

Compare:

• To jest długie. = It is long. → adjective
• Czekam długo. = I wait a long time. → adverb
• Czekam dłużej. = I wait longer. → comparative adverb

Not necessarily.

In English, longer often implies an understood comparison, and the same is true in Polish. Dłużej can mean:

• longer than before
• longer than usual
• longer than expected

All of that can be understood from context.

If you want to make the comparison explicit, you can add:

• niż = than

For example:

• Smażę ją dłużej niż zwykle. = I’m frying it longer than usual.

But in your sentence, the comparison is left implicit, which is very natural.

Because na patelni means in/on the pan as a location, and after na in a location meaning, Polish uses the locative case.

So:

• na patelni = in/on the pan

The noun patelnia changes in the locative:

• patelnia → na patelni

This is similar to:

• na stole = on the table
• na ulicy = on the street
• na talerzu = on the plate

With frying, English says in the pan, but Polish uses na patelni, literally on the pan, which is just the normal Polish expression.

The difference is location versus movement.

• na patelni = on/in the pan → location, so locative
• na patelnię = onto the pan → direction/movement, so accusative

Examples:

• Cebula jest na patelni. = The onion is in the pan.
• Kładę cebulę na patelnię. = I’m putting the onion into/onto the pan.

In your sentence, the onion is already being fried there, so the location form na patelni is correct.

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

The sentence:

• Ta cebula jest jeszcze twarda, więc smażę ją dłużej na patelni.

is neutral and natural.

But other orders are also possible, depending on emphasis. For example:

• Ta cebula jest jeszcze twarda, więc dłużej ją smażę na patelni.
• Ta cebula jest jeszcze twarda, więc na patelni smażę ją dłużej.

These are all grammatically possible, but the original version sounds the most natural in an ordinary context.

Polish often moves words around to change emphasis rather than basic meaning.

A rough pronunciation guide is:

• Ta cebula jest jeszcze twarda, więc smażę ją dłużej na patelni.
• approximately: ta tseh-BOO-la yest YESH-cheh TVAR-da, vyents SMA-zhen yown DWOO-zhei na pa-TEL-nyi

A few helpful points:

• c = ts
• cz = like ch in chop, but harder
• j = English y
• ż/rz = like the s in measure
• ą and ę are nasal vowels, though in real speech they often sound less fully nasal depending on context
• sz = sh

Especially useful here:

• jeszcze sounds roughly like YESH-cheh
• smażę sounds roughly like SMA-zheh
• dłużej sounds roughly like DWOO-zhei
• patelni sounds roughly like pa-TEL-nyi

Yes. Cebula is the normal everyday Polish word for onion.

Depending on context, it can mean:

• onion as a vegetable in general
• one onion
• the onion currently being cooked

In your sentence, Ta cebula means this onion — most naturally, the onion being cooked right now.

So there is nothing unusual about using cebula here.