Sprzedawczyni powiedziała, że dziś najtańsze są białe róże, ale ich zapach jest mniej delikatny.

Sprzedawczyni means female shop assistant / saleswoman / female seller.

Polish often distinguishes masculine and feminine job titles:

• sprzedawca = a male seller / salesman
• sprzedawczyni = a female seller / saleswoman

Because the speaker is referring to a woman, the feminine noun sprzedawczyni is used.

Because the verb in the past tense agrees with the gender of the subject.

The subject is sprzedawczyni, which is feminine, so the verb must also be feminine:

• powiedział = he said
• powiedziała = she said

So:

• Sprzedawczyni powiedziała = The saleswoman said

Że means that and introduces a subordinate clause.

So:

• powiedziała, że... = she said that...

It works much like English that in:

• She said that...

In everyday English, that is often omitted, but in Polish że is normally expressed.

Dziś and dzisiaj both mean today.

The difference is mostly stylistic:

• dziś = a bit shorter, often slightly more concise or literary
• dzisiaj = very common in everyday speech

In this sentence, either would work:

• że dziś najtańsze są...
• że dzisiaj najtańsze są...

Both are natural.

Najtańsze is the superlative form of tani (cheap), so it means the cheapest.

Formation:

• tani = cheap
• tańszy = cheaper
• najtańszy = the cheapest

Here it appears as najtańsze because it agrees with białe róże, which is:

• plural
• non-masculine-personal
• nominative

So the adjective has to match that form:

• najtańsze są białe róże = white roses are the cheapest

Because białe róże is the subject of the clause, so it is in the nominative plural.

Singular:

• biała róża = a white rose

Plural nominative:

• białe róże = white roses

Both words agree with each other:

• białe matches róże
• both are feminine plural in the nominative

If the phrase had a different grammatical role, the forms could change. For example:

• Nie ma białych róż = There are no white roses
  Here you get białych róż because of the genitive.

Both are possible in Polish.

• Białe róże są najtańsze = a more neutral White roses are the cheapest
• Najtańsze są białe róże = puts more emphasis on the cheapest

Polish word order is more flexible than English, and speakers often move words around for emphasis or information structure.

So this version highlights the idea of which flowers are the cheapest.

Because the subject is plural: białe róże (white roses).

The verb być (to be) must agree in number:

• jest = is
• są = are

So:

• białe róże są najtańsze = white roses are the cheapest

Here ich means their and refers to białe róże.

So:

• ich zapach = their scent

This ich is a possessive form and is normally unchanged:

• ich dom = their house
• ich domy = their houses
• ich róża = their rose
• ich zapach = their scent

So unlike many adjectives and pronouns in Polish, ich often stays the same.

Because the sentence is talking about the scent of the roses as a whole, not separate individual scents.

So:

• ich zapach = their scent

This is very natural in both Polish and English. Compare:

• These flowers are beautiful, but their scent is weak.

Even though the flowers are plural, scent can still be singular when treated as one overall characteristic.

Because zapach is singular masculine, and the predicate adjective must agree with it.

• zapach = masculine singular
• so the adjective is delikatny
• and the verb is jest

So:

• zapach jest delikatny = the scent is delicate
• zapach jest mniej delikatny = the scent is less delicate

Everything agrees with zapach, not with róże.

Because mniej delikatny means less delicate, not more delicate.

There are two different ideas:

• delikatniejszy = more delicate
• mniej delikatny = less delicate

So Polish uses:

• bardziej + adjective = more...
• mniej + adjective = less...

Examples:

• bardziej delikatny = more delicate
• mniej delikatny = less delicate

In this sentence, the meaning is specifically less delicate, so mniej delikatny is the correct form.

Yes. Ale is the normal Polish word for but.

It connects two contrasting ideas:

• the white roses are the cheapest
• but their scent is less delicate

So:

• ..., ale ... = ..., but ...

It is one of the most common conjunctions in Polish.