Najpierw rozgrzewam olej, a dopiero potem wrzucam cebulę i warzywa.

Because Polish usually drops subject pronouns when the verb already makes the subject clear.

Here, the endings -am in rozgrzewam and wrzucam tell you the subject is I. So:

• rozgrzewam = I heat / I am heating
• wrzucam = I throw in / I add

You can add ja, but then it sounds emphatic, like I do this first.

In Polish, the present tense is often used for:

• what someone is doing right now
• a habitual action
• step-by-step narration, especially in cooking or instructions

So this sentence can sound like someone describing their cooking process live: First I heat the oil, and only then I add the onion and vegetables.

This is very natural in Polish recipe-style language.

They are imperfective because the speaker is describing the process as it happens, or as a regular procedure.

In Polish:

• imperfective present can describe a current or repeated action
• perfective present usually has future meaning

So:

• rozgrzewam = I heat / I am heating
• wrzucam = I throw in / I am throwing in

But:

• rozgrzeję
• wrzucę

would usually mean I will heat up and I will throw in.

For a live description or cooking explanation, the imperfective forms are the normal choice.

A often links two clauses with a sense of contrast, progression, or sequence. In this sentence, it helps show that the second step comes after the first one.

So najpierw ..., a potem ... is a very natural pattern in Polish.

Compare:

• i = simple and
• a = and / whereas / and then, often with a slight contrast or step-by-step feel

Here, a fits the idea of:

• first one thing happens
• then, after that, the next thing happens

So a sounds better than i in this kind of sequencing.

Dopiero adds emphasis: only then, not until then.

So a dopiero potem is stronger than just a potem.

Compare:

• potem = then / afterwards
• dopiero potem = only then / only afterwards

It suggests that the second action should wait until the first one has been done. In cooking, that kind of timing matters, so dopiero is very natural here.

Because cebulę is the accusative singular form, and it is the direct object of wrzucam.

Base form:

• cebula = onion

After a verb like wrzucam, you need the direct object form:

• wrzucam cebulę = I add / throw in the onion

This is a very common pattern with feminine nouns ending in -a:

• nominative: cebula
• accusative: cebulę

Because different noun types behave differently in the accusative.

In this sentence, all three nouns are direct objects, but their forms do not all change visibly:

• olej → olej
  masculine inanimate noun, so accusative looks like nominative

• cebula → cebulę
  feminine singular noun, so the ending changes

• warzywa → warzywa
  plural non-masculine-personal noun, where nominative and accusative are the same

So even though all three are objects, only cebula shows an obvious ending change here.

Yes, it is very natural.

Literally, wrzucać does mean to throw in, but in cooking it is commonly used in a broader, idiomatic way: to put in, to toss in, to add.

So wrzucam cebulę i warzywa sounds like natural spoken Polish in a kitchen context.

A slightly more neutral alternative would be:

• dodaję cebulę i warzywa = I add the onion and vegetables

But wrzucam is absolutely normal and common.

Polish word order is flexible, and here the speaker puts the time words first for emphasis:

• Najpierw = first
• dopiero potem = only then

That makes the sequence very clear from the start of each clause.

So the sentence structure highlights the order of actions:

• first: heat the oil
• only then: add the onion and vegetables

You could move words around in Polish, but this version sounds very natural and clear, especially for instructions or narration.

Correct: Polish has no articles.

So nouns like:

• olej
• cebulę
• warzywa

do not have separate words for the or a/an. Whether the meaning is definite or indefinite is understood from context.

Depending on the situation, cebulę could mean:

• an onion
• the onion

and olej could mean:

• oil
• the oil

English requires articles, but Polish normally does not use them.

Yes, in standard Polish it is.

That is because a is connecting two clauses, each with its own finite verb:

• rozgrzewam
• wrzucam

So the comma helps separate the two parts:

• Najpierw rozgrzewam olej, a dopiero potem wrzucam cebulę i warzywa.

This punctuation is normal and expected.