Czytelnik obok mnie czytał krótki wiersz, a potem zapisał jeden akapit w zeszycie.

Because obok takes the genitive case. The pronoun ja changes to mnie in the genitive.

So:

• ja = I
• obok mnie = next to me / beside me

This is a fixed grammar pattern:

• obok domu = next to the house
• obok szkoły = next to the school
• obok mnie = next to me

It describes where the reader was: beside me / next to me.

So Czytelnik obok mnie means:

• the reader next to me
• or more literally, the reader beside me

It functions like a description attached to czytelnik.

This is about aspect, which is very important in Polish.

• czytać = imperfective, focuses on the process of reading
• przeczytać = perfective, focuses on finishing reading something

So:

• czytał krótki wiersz = he was reading / he read a short poem
  (the action itself is being described, not necessarily its completion)
• przeczytał krótki wiersz = he read through / finished a short poem

In this sentence, czytał presents the reading as an activity, while zapisał later presents a completed action.

Again, this is aspect.

• pisać = to write, imperfective
• zapisać = to write down, to note down, perfective

So zapisał jeden akapit suggests a completed result: he wrote down one paragraph.

Compare:

• pisał akapit = he was writing a paragraph / he used to write a paragraph
• zapisał akapit = he wrote down a paragraph and completed that act

Because they present the two actions differently:

• czytał shows the reading as an ongoing activity
• zapisał shows the writing-down as a completed action

This is very natural in Polish. The sentence is not just about past time; it also shows how each action is viewed.

A rough nuance is:

• he was reading a short poem,
• and then he wrote down one paragraph.

Krótki wiersz is in the accusative case, because it is the direct object of czytał.

However, for a masculine inanimate noun, the accusative often looks exactly like the nominative.

So:

• nominative: krótki wiersz
• accusative: krótki wiersz

That is why the form does not change here.

It is also in the accusative case, because it is the direct object of zapisał.

And again, akapit is masculine inanimate, so the accusative looks like the nominative:

• nominative: jeden akapit
• accusative: jeden akapit

So the form stays the same.

It literally means one paragraph, but in context it can also feel like a single paragraph.

Polish has no articles like a or the, so jeden sometimes adds emphasis similar to one or a certain single.

Here it most naturally suggests:

• one paragraph
• a single paragraph

It is a bit more specific than just akapit.

Because the preposition w meaning in requires the locative case when talking about location.

• zeszyt = notebook
• locative singular: zeszycie

So:

• w zeszycie = in the notebook

This is a very common pattern:

• w domu = in the house
• w szkole = at school / in the school
• w zeszycie = in the notebook

Both are possible, but a potem is very natural when linking one event to the next.

• a often connects clauses with a sense of moving on, contrast, or sequence
• potem = then / afterwards

So a potem means:

• and then
• and afterwards

It sounds very normal in storytelling:

• first this happened,
• and then that happened.

From the past-tense verb forms:

• czytał
• zapisał

The ending -ał marks masculine singular in the past tense.

Compare:

• czytał / zapisał = he
• czytała / zapisała = she
• czytało / zapisało = it
• czytali / zapisali = they (at least one male or mixed group)
• czytały / zapisały = they (all non-masculine-personal)

Also, czytelnik itself is a masculine noun.

Yes. Polish often drops subject pronouns when the verb already shows who is acting.

So instead of saying On czytał..., Polish normally just says:

• Czytał krótki wiersz...

In this sentence, the noun Czytelnik is stated explicitly because it introduces who the person is:

• Czytelnik obok mnie...

After that, adding on would usually be unnecessary.

Yes. Polish word order is fairly flexible, though the default order here is natural and clear.

The original:

• Czytelnik obok mnie czytał krótki wiersz, a potem zapisał jeden akapit w zeszycie.

Other possible orders include:

• Obok mnie czytelnik czytał krótki wiersz, a potem zapisał jeden akapit w zeszycie.
• Czytelnik czytał obok mnie krótki wiersz, a potem zapisał jeden akapit w zeszycie.

These versions may slightly change the emphasis, but the basic meaning stays the same.

Yes, in many contexts obok mnie and koło mnie both mean next to me / beside me.

However:

• obok mnie is often a bit more neutral and precise
• koło mnie is also very common in everyday speech

So you could say:

• Czytelnik obok mnie...
• Czytelnik koło mnie...

Both are natural.

Good question. They are related but not identical.

• zapisać often means to write down, to note down, to record in writing
• napisać often means to write/create something

So:

• zapisał jeden akapit w zeszycie = he wrote down one paragraph in the notebook
• napisał jeden akapit = he wrote one paragraph

In this sentence, zapisał suggests putting something into the notebook, perhaps copying or noting it down.

Not necessarily.

Because czytał is imperfective, it focuses on the act of reading, not on completion. It can imply that he was engaged in reading the poem, but it does not strongly state that he finished it.

If you want to clearly show completion, Polish would more likely use:

• przeczytał krótki wiersz

So the original leaves the reading action less bounded than the writing action.