Learn Hardcore Polish: Na biurku leży kartka z hasłem do konta, które właśnie utworzyłem. - On the desk there is a note with the password for the account that I have just created.

In Polish, jest (“is”) is the general existential verb (“there is”), whereas leżeć (“to lie”) describes something resting in a horizontal position. Since a kartka (piece of paper) physically lies flat on the desk, leży is more precise. You could say Na biurku jest kartka, but Na biurku leży kartka paints a clearer picture of how the paper sits.

Can I change the word order, for example say Kartka leży na biurku? Does it change anything?

Polish word order is quite flexible. All of these are correct:

Kartka leży na biurku. (neutral statement)
Na biurku leży kartka. (emphasizes the location “On the desk…”)
Leży kartka na biurku. (even more poetic or to draw attention to the paper)

The basic meaning stays the same, but what you put first becomes the topic or focus of the sentence.

Why is z hasłem in the instrumental case, and do konta in the genitive case?

Polish prepositions require specific cases:

z (“with”) always takes the instrumental → z hasłem (hasło → hasłem).
do (“to/for”) always takes the genitive → do konta (konto → konta).

So kartka z hasłem do konta literally means “a piece of paper with the password for the account.”

Why is the relative pronoun które used here, and how does it agree with konto?

który is the Polish relative pronoun (“which/that”). It must match its antecedent (konto) in gender, number, and case:

konto is neuter singular.
In the clause które właśnie utworzyłem, konto is the direct object of utworzyć, so the pronoun is in the accusative—but in neuter singular nominative = accusative = które.

Why is utworzyłem perfective, and what does its ending -łem tell us about the speaker?

utworzyłem is the past tense of the perfective verb utworzyć (“to create”; completed action). Using perfective here (właśnie utworzyłem) stresses that you “have just created” the account. The ending -łem marks first person singular masculine. A female speaker would say utworzyłam. If you wanted to describe an ongoing or repeated action, you’d use the imperfective tworzyć:

właśnie tworzyłem – “I was just creating.”

What does właśnie mean, and can it appear in a different position?

właśnie means “just” (emphasizing that something happened very recently) or “exactly.” It’s an adverb with flexible placement, often right before the verb in Polish:

Właśnie utworzyłem konto.
Utworzyłem właśnie konto.

In the original sentence, it sits in the relative clause before the verb: które właśnie utworzyłem. You could move it to które utworzyłem właśnie, but that sounds less natural in this context.