Ta sprzedawczyni jest miła, ale nasza kierowniczka jest dziś bardzo zajęta.

Because both sprzedawczyni and kierowniczka are feminine singular nouns.

In Polish, words like this and our must agree with the noun in gender, number, and usually case:

• ta = this for a feminine singular noun
• nasza = our for a feminine singular noun

Compare:

• ta sprzedawczyni = this saleswoman / this shop assistant
• ten sprzedawca = this salesman
• ta kierowniczka = this female manager
• ten kierownik = this male manager

So the forms are feminine because the nouns are feminine.

Because they are adjectives describing feminine singular nouns.

• sprzedawczyni is feminine singular, so miła must also be feminine singular.
• kierowniczka is feminine singular, so zajęta must also be feminine singular.

This is adjective agreement.

Compare:

• masculine: miły, zajęty
• feminine: miła, zajęta
• neuter: miłe, zajęte

So:

• sprzedawczyni jest miła
• kierowniczka jest zajęta

both use feminine adjective forms.

The nouns sprzedawczyni and kierowniczka are in the nominative singular, because they are the subjects of the sentence.

The adjectives miła and zajęta are also in forms that agree with those feminine singular subjects.

A useful thing to remember:

• with być (to be), adjectives like miła and zajęta stay in the agreeing form
• predicate nouns in Polish are sometimes nominative or instrumental depending on structure, but here we are dealing with adjectives, not nouns

So in this sentence, learners should mainly notice feminine singular agreement.

It is used twice because the sentence has two clauses:

• Ta sprzedawczyni jest miła
• ale nasza kierowniczka jest dziś bardzo zajęta

In normal Polish, you keep jest in both parts. Leaving it out would sound incomplete or unnatural in standard speech.

So this repetition is normal:

• X jest ... , ale Y jest ...

It works just like English is ... but ... is ...

Ale means but, so it clearly marks a contrast.

Here the contrast is:

• the saleswoman is nice
• but the manager is very busy today

You could sometimes use a in Polish for a softer contrast or simple linking, something like and / while / whereas, depending on context. But ale is stronger and more clearly means but.

So:

• ale = stronger contrast, but
• a = often a milder contrast or a linking and/while

In this sentence, ale is very natural.

Sprzedawczyni means a female salesperson, saleswoman, or female shop assistant, depending on context.

It is specifically feminine.

Related forms:

• sprzedawca = salesman / seller / male sales assistant
• sprzedawczyni = saleswoman / female sales assistant

English often does not mark gender as strongly in job titles, but Polish often does.

Also, sprzedawczyni is one of those feminine nouns that does not end in -a, even though it is feminine.

Yes. Kierowniczka is specifically female.

It means something like:

• female manager
• female supervisor
• female person in charge

The masculine counterpart is:

• kierownik = male manager / supervisor

So in this sentence, nasza kierowniczka means our female manager/supervisor.

Dziś means today.

Its placement is flexible, because Polish word order is more flexible than English. In this sentence, jest dziś bardzo zajęta sounds very natural and neutral.

You could also say:

• Nasza kierowniczka jest dziś bardzo zajęta.
• Dziś nasza kierowniczka jest bardzo zajęta.

Both are correct. The second one puts more emphasis on today.

So the sentence you have uses a very normal, neutral placement.

Yes, basically.

• dziś = today
• dzisiaj = today

They mean the same thing. Dziś is just a shorter form, and it is very common.

So:

• jest dziś zajęta
• jest dzisiaj zajęta

both are correct.

Bardzo means very.

It strengthens the adjective zajęta:

• zajęta = busy
• bardzo zajęta = very busy

This is the normal position:

• bardzo
  • adjective

Examples:

• bardzo miła = very nice
• bardzo zajęta = very busy
• bardzo zmęczona = very tired

No. Polish word order is fairly flexible, although some orders sound more neutral than others.

The given sentence is a very natural, standard order:

• Ta sprzedawczyni jest miła, ale nasza kierowniczka jest dziś bardzo zajęta.

You could move some elements for emphasis, especially dziś:

• Ta sprzedawczyni jest miła, ale dziś nasza kierowniczka jest bardzo zajęta.
• Dziś nasza kierowniczka jest bardzo zajęta.

But not every rearrangement sounds equally natural. The original version is a good model to learn first.

Because Polish does not have articles like English the and a/an.

So:

• sprzedawczyni can mean a saleswoman or the saleswoman
• kierowniczka can mean a manager or the manager

The exact meaning depends on context.

In this sentence, ta helps make the first noun more specific:

• ta sprzedawczyni = this saleswoman / this shop assistant

And nasza kierowniczka is also specific because our manager is already definite in meaning.

A rough pronunciation guide is:

• sprzedawczyni ≈ pshe-da-f-CHI-nih
• kierowniczka ≈ kye-rov-NICH-ka
• zajęta ≈ za-YEN-ta

A few useful sound notes:

• sz sounds roughly like English sh
• cz sounds roughly like ch in chop, but harder
• w in Polish sounds like English v
• ń is a soft n sound
• stress is usually on the second-to-last syllable

So:

• sprze-daw-czy-ni
• kie-row-nicz-ka
• za-ję-ta

A rough guide is helpful, but listening to native audio is best.