Kasjerka przy tej kasie pracuje bardzo szybko.

Kasjerka is the feminine noun, meaning female cashier.
Kasjer is the masculine form, meaning male cashier.

So this sentence specifically refers to a woman:

• kasjerka = female cashier
• kasjer = male cashier

If the cashier were a man, the sentence would be:

• Kasjer przy tej kasie pracuje bardzo szybko.

It means at this checkout / at this cash register / at this till.

• przy = by, near, at
• tej kasie = this checkout/register in the form required after przy

In a shop context, kasa usually means:

• cash register
• checkout
• till

So przy tej kasie is a natural way to say someone is working at this register.

Because the preposition przy requires the locative case in Polish.

Base form:

• ta kasa = this register / this checkout

After przy, it changes:

• przy tej kasie = at this register

So:

• ta → tej
• kasa → kasie

This is a very common pattern in Polish: the preposition determines the case of the noun phrase that follows it.

Yes, przy is one of the prepositions that takes the locative case.

Examples:

• przy stole = at the table
• przy oknie = by the window
• przy tej kasie = at this checkout

So if you see przy, you should expect the following noun to be in the locative.

Pracuje is the 3rd person singular present tense of pracować (to work).

Conjugation:

• ja pracuję = I work
• ty pracujesz = you work
• on/ona pracuje = he/she works

Since the subject is kasjerka (she / the female cashier), the verb is:

• kasjerka pracuje = the cashier works

Because szybko is an adverb, and it modifies the verb pracuje.

• szybki / szybka / szybkie = fast as an adjective
• szybko = fast / quickly as an adverb

Here we are describing how she works, not what kind of person she is:

• pracuje szybko = she works quickly

If you said szybka kasjerka, that would mean:

• a fast cashier

So:

• kasjerka jest szybka = the cashier is fast
• kasjerka pracuje szybko = the cashier works quickly

Because bardzo means very, and it strengthens the adverb szybko.

So:

• szybko = quickly / fast
• bardzo szybko = very quickly / very fast

This works like English:

• She works quickly
• She works very quickly

Yes. In natural English, both can work depending on style.

Polish uses:

• szybko as an adverb

English can say:

• works very quickly
• works very fast

Both are natural translations here.

Not exactly. In this sentence, kasa means cash register / till / checkout, not just cash as money.

Depending on context, kasa can sometimes refer to money in informal speech, but here przy tej kasie clearly means:

• at this register
• at this checkout

So you should understand kasa here as a place or machine where payment is handled.

It can mean both, depending on context.

Kasjerka przy tej kasie pracuje bardzo szybko can mean:

• she is working very quickly now
• she generally works very quickly
• the cashier at this register is a fast worker

Polish present tense often covers both:

• a current action
• a habitual or general fact

So context tells you whether it is about right now or in general.

Because Polish has no articles like the or a/an.

English says:

• The cashier
• A cashier

Polish usually just says:

• kasjerka

Specificity is understood from context or shown in other ways, for example with:

• ta / ten / to = this/that
• word order
• context

In this sentence, tej makes the checkout specific:

• przy tej kasie = at this checkout

But kasjerka itself still has no article.

Yes. Polish word order is more flexible than English, although the neutral order here is perfectly natural.

Original:

• Kasjerka przy tej kasie pracuje bardzo szybko.

Possible alternatives:

• Przy tej kasie kasjerka pracuje bardzo szybko.
• Kasjerka pracuje przy tej kasie bardzo szybko.
• Bardzo szybko pracuje kasjerka przy tej kasie.

These versions may sound different in emphasis, but the basic meaning stays similar.

The original sentence sounds like a normal, neutral statement.

In a neutral reading, the sentence simply gives information:

• Kasjerka przy tej kasie pracuje bardzo szybko.

But Polish can shift emphasis by changing word order.

For example:

• Przy tej kasie kasjerka pracuje bardzo szybko.
  This puts more focus on at this checkout.
• Kasjerka przy tej kasie bardzo szybko pracuje.
  This can put a bit more focus on very quickly.

So the original version is a good standard sentence, while other orders may highlight different parts.

Usually no, not in this meaning.

• przy tej kasie = at this checkout / by this register
• w tej kasie would literally mean in this register / in this checkout, which is not what you want here

When talking about a cashier physically working at a till, przy kasie is the normal expression.

A simple approximation for an English speaker:

• kasjerka ≈ kah-SYER-kah
• kasie ≈ KAH-shyeh or KAH-syeh depending on how carefully you pronounce it

A few useful notes:

• a is like a in father
• j in Polish sounds like English y in yes
• si before a vowel often sounds like a soft sh / sy sound
• ie is usually pronounced as a separate vowel sound, not like English ee

So:

• kasjerka has a soft middle sound: -sjer-
• kasie is not pronounced like English casey

The dictionary form is kasa.

Here is the pattern:

• kasa = nominative singular
• kasie = locative singular

So if you look the word up in a dictionary, you need to search for:

• kasa

This is very common in Polish: the form you see in a sentence is often not the dictionary form because of case endings.

It usually refers to the cashier working at that specific register, but Polish leaves some things to context.

Because there is no article, kasjerka could be understood as:

• the cashier
• a cashier

But in real context, przy tej kasie makes it sound like a specific person at a specific checkout:

• The cashier at this register works very quickly

So in most situations, that is the most natural understanding.