Kasjerka przy tej kasie podaje mi paragon i resztę.

A word-by-word breakdown:

• Kasjerka = female cashier
• przy = by / at / next to
• tej kasie = this checkout / this cash register
  
  • from ta kasa
• podaje = gives / hands
• mi = to me
• paragon = receipt
• i = and
• resztę = change (money returned after payment)

So grammatically, the sentence is structured like:

• Kasjerka = subject
• przy tej kasie = location
• podaje = verb
• mi = indirect object
• paragon i resztę = direct objects

Because przy requires the locative case.

The basic form is:

• ta kasa = this cash register / this checkout

But after przy, both words change into locative:

• ta → tej
• kasa → kasie

So:

• przy tej kasie = at/by this checkout

This is a very common Polish pattern:

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

In this sentence, przy tej kasie most naturally means:

• at this checkout
• at this cash register
• possibly by this till

In a shop context, kasa can mean:

• the actual cash register machine
• the checkout point/lane

So kasjerka przy tej kasie means the cashier working at that specific checkout.

Both can mean to me, but mi is the normal unstressed short form.

Here, mi is in the dative case, because the cashier is giving something to me:

• podaje mi paragon = she hands me the receipt

Use mi in ordinary neutral sentences.
Use mnie more for emphasis, contrast, or after some prepositions.

Compare:

• Kasjerka podaje mi paragon. = neutral
• Kasjerka podaje mnie paragon. = incorrect
• Kasjerka podaje mnie? = incorrect in this meaning
• Mnie podaje paragon, nie tobie. = To me she gives the receipt, not to you.
  Here mnie is emphatic.

Because resztę is the accusative singular form of reszta.

In this sentence, reszta means change (money returned after paying). It is a direct object of podaje, so it goes into the accusative:

• reszta = nominative
• resztę = accusative

That is why we get:

• podaje ... resztę = gives ... the change

This is very common with feminine nouns ending in -a:

• kawa → kawę
• woda → wodę
• reszta → resztę

Because paragon is a masculine inanimate noun, and for many masculine inanimate nouns, the accusative singular looks the same as the nominative singular.

So:

• nominative: paragon
• accusative: paragon

That is why:

• podaje paragon = gives the receipt

Compare with another masculine inanimate noun:

• stół = table
• widzę stół = I see the table

But not all nouns behave identically across all declensions, so it is best to learn the general pattern and then confirm specific nouns as you go.

Podaje is 3rd person singular present tense of podawać.

It can mean either:

• gives
• is giving / is handing

Which English translation sounds best depends on context.

Polish present tense often covers both:

• a habitual action
• an action happening right now

So this sentence could mean:

• The cashier at this checkout gives me the receipt and the change.
• The cashier at this checkout is handing me the receipt and the change.

The verb podawać is imperfective. Its rough perfective partner is podać.

In the present tense:

• podaje = present-time action, ongoing/repeated/neutral description
• poda = future, because perfective verbs do not normally have a true present meaning in Polish

So if you say:

• Kasjerka podaje mi paragon i resztę
  you are describing what is happening or what usually happens.

If you say:

• Kasjerka poda mi paragon i resztę
  that means The cashier will give me the receipt and change.

That is why podaje is the right form here.

Yes, Polish word order is flexible.

The sentence starts with Kasjerka because that is a natural neutral way to introduce the subject first:

• Kasjerka przy tej kasie podaje mi paragon i resztę.

But other orders are possible, depending on emphasis:

• Przy tej kasie kasjerka podaje mi paragon i resztę.
  Emphasis on the location.
• Paragon i resztę podaje mi kasjerka przy tej kasie.
  Emphasis on what is being handed over.
• Mi kasjerka przy tej kasie podaje paragon i resztę.
  Possible, but more marked.

So the original order is a very natural, neutral sentence.

Yes. Kasjerka is specifically female cashier.

The masculine form is:

• kasjer = male cashier

So:

• Kasjerka podaje mi paragon. = The female cashier gives me the receipt.
• Kasjer podaje mi paragon. = The male cashier gives me the receipt.

In Polish, job titles often show grammatical gender more clearly than in English.

Yes, if the context already makes it obvious who receives the receipt and change.

For example:

• Kasjerka podaje paragon i resztę.
  = The cashier gives the receipt and the change.

But including mi makes it explicit that the cashier is giving them to me.

So:

• with mi = clearer and more personal
• without mi = still grammatical, but less specific

No. Reszta has a broader meaning: the rest / remainder.

Examples:

• reszta pieniędzy = the rest of the money
• reszta dnia = the rest of the day
• poproszę resztę = I’d like the change

In a shopping/payment context, reszta very often means change.
So in this sentence, that is definitely the intended meaning.

Yes, it is understandable, but podaje is more natural here.

• daje = gives
• podaje = hands over / passes / gives in a more specific physical sense

At a checkout, when a cashier hands you a receipt and change, podaje sounds very natural because it suggests physically passing the items to you.

So:

• daje mi paragon i resztę = correct, more general
• podaje mi paragon i resztę = very natural in this situation