Learn Hardcore Russian: Оплаченный счёт лежит в папке на столе. - The paid bill is in the folder on the table.

Оплаченный is a past passive participle from the verb оплатить (to pay). In this sentence it behaves like an adjective and agrees with the noun:

оплаченный (masc. nom. sg.) + счёт (masc. nom. sg.) Meaning: the paid bill/invoice.

Why is it оплаченный счёт and not оплачен счёт?

Russian has two common participle/adjective-style options:

оплаченный счёт = “the paid bill” (long form; describes the noun like an adjective; very common in writing and speech)
счёт оплачен / счёт был оплачен = “the bill is/was paid” (short form used predicatively, like a statement about the bill)

Your sentence uses the attributive version (оплаченный) to label which bill it is.

What case is счёт in, and why?

Счёт is nominative singular because it is the subject of лежит (“lies/is lying”):

(Что?) счёт лежит = “(What?) the bill is lying…”

What does счёт mean here: “account” or “bill”?

In this context (Оплаченный счёт, in a folder, on a table), счёт almost certainly means a bill / invoice (a document you pay). Счёт can also mean:

account (bank account) in phrases like банковский счёт
score/count in phrases like счёт 2:1

Context determines it.

Why is it лежит (“lies”) and not “is” / находится?

Russian often uses posture/location verbs where English might use “is”:

лежит = “is lying / is (lying) there” (a natural verb for papers, documents, objects placed flat) Alternatives you might also hear:
находится (more formal/neutral: “is located”)
лежит is especially idiomatic for documents: Счёт лежит в папке.

Why is it в папке (with в)?

в + prepositional case means “in/inside” when talking about location:

в папке = “in the folder” Here папке is prepositional singular of папка.

(If you meant motion “into the folder,” it would be в папку with accusative.)

Why is it на столе and not на стол?

Because this is location, not motion:

на
- prepositional = “on (top of), located on” → на столе
на
- accusative = “onto” (movement) → на стол

So:

лежит на столе = “is lying on the table”
положил на стол = “put (it) onto the table”

Does на столе describe the folder or the bill? Is the sentence ambiguous?

Normally в папке на столе is understood as one unit: “in the folder (that is) on the table.”
So the default meaning is:

the bill is inside the folder
the folder is on the table

If you wanted to force “the bill is in the folder, and the bill is on the table” (odd), you’d usually rephrase.

What’s the most natural word order? Can I move things around?

Yes. Russian word order is flexible, and changes what feels “new” or emphasized:

Оплаченный счёт лежит в папке на столе. (neutral)
В папке на столе лежит оплаченный счёт. (emphasis on location; answers “Where is it?”)
Оплаченный счёт лежит на столе в папке. (possible, but less smooth; can sound like you’re adding details step by step)

How do I pronounce счёт and what is the spelling issue with ё?

счёт is pronounced roughly like shchyot (one syllable), with ё = yo.
In many texts, ё is often written as е, so you may see счет, but it’s the same word; the intended pronunciation is usually still счёт in this meaning.

Could I replace оплаченный with a verb phrase like “has been paid”?

Yes, and the meaning stays close:

Счёт оплачен. = “The bill is paid.”
Счёт был оплачен. = “The bill was paid.”
Они оплатили счёт. = “They paid the bill.” (active, specifies an agent)

Using оплаченный счёт keeps it compact and “document-like,” which is common for paperwork contexts.