U pokladny se mě ptají, jestli chci účtenku.

U pokladny means at the checkout / at the cash register.

The preposition u usually means by, near, at, and it requires the genitive case.
That is why pokladna becomes pokladny:

• pokladna = checkout, cash register
• u pokladny = at the checkout

So this is a normal preposition + case combination:

• u školy = by the school
• u domu = by the house
• u pokladny = at the checkout

In this sentence, se is part of the verb ptát se, which means to ask.

So:

• ptát by itself is not the normal dictionary form for to ask
• the full verb is ptát se

Examples:

• Ptám se. = I ask / I am asking.
• Ptají se mě. = They ask me.

Here, se does not mean themselves. It is just a built-in part of the verb.

This is common in Czech. Many verbs include se or si:

• dívat se = to look
• bát se = to be afraid
• ptát se = to ask

Mě is the form of I / me used here because the verb ptát se takes the person being asked in the genitive.

So:

• já = I
• mě / mne = me

With ptát se, you ask someone:

• Ptají se mě. = They ask me.
• Ptají se tě. = They ask you.
• Ptají se ho. = They ask him.

So mě is correct because it means me, and that is the form this verb requires.

That is a very good question. Czech verbs do not all govern the same case.
The verb ptát se is one of the verbs that traditionally takes the genitive for the person asked.

So:

• ptát se koho / čeho = to ask whom / about what

Examples:

• Ptám se učitele. = I ask the teacher.
• Ptají se mě. = They ask me.
• Ptal se jí. = He asked her.

This is just something you learn together with the verb:

• ptát se + genitive

At the same time, the thing being asked about can be introduced in other ways, for example:

• Ptají se mě na cenu. = They ask me about the price.

In Czech, just like in English, you can use they in a general, unspecified way.

Here, ptají is 3rd person plural:

• oni se ptají = they ask

But the sentence does not need to say oni, because Czech often leaves subject pronouns out when the verb ending already shows the person.

So:

• U pokladny se mě ptají...
  literally: At the checkout they ask me...

In natural English, this often becomes:

• At the checkout, they ask me...
• At the checkout, I’m asked...
• At the checkout, they ask whether I want a receipt.

The hidden they means something like the cashier / the staff / people there.

Not grammatically, no. It is an active sentence with an unspecified they.

• se mě ptají = they ask me

However, in English, we often translate this kind of sentence with a passive because it sounds natural:

• At the checkout, I’m asked if I want a receipt.

So the Czech is active, but the English translation may be active or passive depending on style.

Yes. Here jestli means if / whether in an indirect question.

• ptají se mě, jestli chci účtenku
  = they ask me if / whether I want a receipt

This is not the same kind of if as in a condition like:

• If it rains, I’ll stay home.

In Czech:

• jestli = if / whether in indirect questions
• když or jestli can sometimes appear in conditions in everyday speech, but here it is clearly whether

You could also sometimes see zda, which is a bit more formal:

• Ptají se mě, zda chci účtenku.

Chci is the 1st person singular form of chtít, meaning to want.

Conjugation:

• chci = I want
• chceš = you want
• chce = he/she/it wants
• chceme = we want
• chcete = you want
• chtějí / chcou = they want

So:

• jestli chci účtenku = if I want a receipt

You may also hear chcu in some regions, especially in Moravia, but chci is the standard form taught to learners.

Because účtenka is the direct object of chci, so it goes into the accusative case.

• účtenka = nominative
• účtenku = accusative

This is a regular pattern for many feminine nouns ending in -a:

• kniha → knihu
• káva → kávu
• účtenka → účtenku

So:

• Chci účtenku. = I want a receipt.

Yes, účtenka usually means receipt.

In a shop, if someone asks:

• Chcete účtenku?

they mean:

• Do you want a receipt?

It is the normal everyday word for the printed proof of purchase.

Both are possible. Czech word order is flexible, and it often changes emphasis rather than basic meaning.

• U pokladny se mě ptají, jestli chci účtenku.
  This puts at the checkout first, setting the scene.

• Ptají se mě u pokladny, jestli chci účtenku.
  This starts with the action they ask me.

The version with U pokladny first sounds very natural if you want to emphasize the situation or location first.

No, not in standard Czech.

The correct verb is ptát se, so the se must stay with the verb:

• Ptají se mě. = correct
• Ptají mě. = not standard for this meaning
• Ptají mě se. = incorrect

A useful rule is to learn the whole expression:

• ptát se koho = to ask someone

Both can mean me, and both are correct forms. In most everyday speech, mě is much more common.

So:

• Ptají se mě. = normal, everyday
• Ptají se mne. = also correct, but more formal or stylistically marked

For a learner, mě is the form you will hear and use most often in ordinary conversation.

By itself, it most naturally suggests a general or repeated situation:

• At the checkout, they ask me if I want a receipt.

The present tense in Czech can describe what generally happens in a typical situation.

If you wanted a one-time past event, you would use the past:

• U pokladny se mě ptali, jestli chci účtenku.
  = At the checkout, they asked me if I wanted a receipt.

If you wanted a likely one-time future/perfective meaning, you might use:

• U pokladny se mě zeptají, jestli chci účtenku.
  = At the checkout, they’ll ask me if I want a receipt.

This is mainly a question of aspect.

• ptají se comes from ptát se and is imperfective
• zeptají se comes from zeptat se and is perfective

Very roughly:

• ptají se = they are asking / they ask
• zeptají se = they ask once / they will ask

In your sentence, ptají se works well for a habitual or general situation:

• At the checkout, they ask me...

If you are talking about one specific completed asking event, zeptají se may be more natural.

A rough guide:

• ú is a long oo sound
• č sounds like ch in chair
• t is a normal t
• e is like e in bed
• n is n
• k is k
• u is a short oo

So approximately:

• OOCH-ten-koo

Stress in Czech is normally on the first syllable, so:

• Účtenku

It can mean both depending on context.

In a shop, pokladna often refers to:

• the cash register itself
• the checkout counter / checkout area

So u pokladny naturally means:

• at the checkout
• at the register

In this sentence, at the checkout is probably the best natural English understanding.