Learn Hardcore Finnish: Asiakas kysyy, missä kassa on. - The customer asks where the checkout is.

Finnish uses a comma to separate a main clause from a subordinate clause. Here, missä kassa on is an indirect question (a subordinate clause), so a comma is mandatory. The whole sentence is a statement, so there is no question mark. Compare:

Tiedätkö, missä kassa on? (main clause is a question, so the sentence ends with a question mark)
Asiakas kysyy, missä kassa on. (main clause is a statement)

Can I say että missä kassa on?

No. Että introduces a declarative content clause (like “that” in English), not an interrogative one. With question words (missä, milloin, miksi, kuka, etc.), you do not use että. Say:

Asiakas kysyy, missä kassa on. But with a declarative:
Asiakas sanoo, että kassa on tuolla.

Why is it missä kassa on and not missä on kassa?

In indirect questions, the neutral word order is: question word + subject + verb, so missä kassa on is preferred. In direct questions, both orders are common:

Missä kassa on?
Missä on kassa? In indirect questions, …missä kassa on sounds more natural and less marked than …missä on kassa.

How would this look in direct speech?

Use a colon and a question mark:

Asiakas kysyy: Missä kassa on? Direct speech keeps the original question punctuation; indirect speech does not.

What exactly does kassa mean here?

Kassa can mean:

the checkout/checkout counter,
the cash register (machine),
the cashier (person), depending on context. In a store context, kassa usually means the checkout. If you specifically mean the machine, you can say kassakone; for the counter: kassatiski.

Why is it missä and not mihin or mistä?

These are different locative questions:

missä = where (static location) → “Where is the checkout?”
mihin/minne = to where (direction towards) → “Where to (which way) is the checkout?”
mistä = from where (direction away) → “Where from is the checkout moving/coming?” (less likely here) For “Where is…?”, use missä.

Why is kassa in the nominative and not kassalla/kassassa?

Kassa is the subject of the embedded clause and stays in the nominative. The location is already expressed by the question word missä. Forms like kassalla (“at the checkout”) or kassassa (“in the cash register”) would be used to describe the location of some other item:

Lompakkoni on kassalla. “My wallet is at the checkout.”

Why does kysyy have a double y?

It’s the regular 3rd person singular present for type-1 verbs (ending in -a/ä in the dictionary form). The final vowel lengthens:

kysyä → kysyy
sanoa → sanoo
puhua → puhuu

If this happened in the past, do I change kysyy and/or on?

Change the main verb for past; the embedded tense depends on what you mean:

Asiakas kysyi, missä kassa on. (He asked earlier, and you still treat the location as current/relevant now.)
Asiakas kysyi, missä kassa oli. (He asked where it was at that past time.) Finnish sequence of tenses is flexible and driven by meaning.

How do I say who the customer asks?

Use kysyä + ablative (-lta/ltä) “ask from someone”:

Asiakas kysyy myyjältä, missä kassa on. “The customer asks the salesperson where the checkout is.”
Kysyin sinulta neuvoa. “I asked you for advice.”

Can I say Asiakas kysyy kassaa?

Not for this meaning. Kysyä + partitive is used for asking for something (advice, help, directions), not for asking about the location of a person/place:

Natural: Asiakas kysyy neuvoa/tietä. (“asks for advice/the way”) To ask about location, use an indirect question: kysyy, missä kassa on.

Why are there no words for “the” or “a” here?

Finnish has no articles. Asiakas and kassa can be interpreted as “a customer/the customer” and “a/the checkout” based on context.

Is the comma mandatory? I sometimes see it omitted.

In standard written Finnish, yes: you must separate the main clause and a following subordinate clause with a comma. In informal texting you may see it dropped, but it’s considered a mistake in formal writing.

Any quick pronunciation tips for this sentence?

y (in kysyy) is a front rounded vowel (like French u); keep it rounded.
ä (in missä) is an open front vowel (like German ä in Mädchen).
Double letters matter: ss in missä and kassa is a long [s], yy in kysyy is a long vowel.
Primary stress is on the first syllable of each word: Á-si-a-kas KY-syy, MÍS-sä KÁS-sa on.