Do tej sukienki pasują czarne rajstopy i buty na niskim obcasie.

Because the preposition do requires the genitive case.

• ta sukienka = this dress (dictionary/basic form, nominative)
• do tej sukienki = to/for this dress or more naturally with this dress

In Polish, pasować do means to match / go with, so the thing after do must be in the genitive:

• ta sukienka → tej sukienki
• ten sweter → tego swetra

So Do tej sukienki pasują... literally means something like To this dress, ... match.

Here pasują means match, go with, or suit.

The verb is pasować. It can be used in a few related ways:

• pasować do czegoś = to match / go with something
• pasować komuś = to suit someone
• sometimes pasować can also mean to fit physically

In this sentence, it is about clothing items matching another item of clothing:

• Do tej sukienki pasują czarne rajstopy...
• Black tights go well with this dress...

So this is not mainly about size, but about style/appearance.

Because the subject is plural:

• czarne rajstopy i buty na niskim obcasie

That means black tights and low-heeled shoes — two things together, so Polish uses a plural verb.

Compare:

• Pasuje czarna torebka. = A black handbag matches.
• Pasują czarne rajstopy. = Black tights match.
• Pasują czarne rajstopy i buty. = Black tights and shoes match.

So pasują is the 3rd person plural form of pasować.

Because Polish word order is much more flexible than English word order.

The most neutral English order would be:

• Black tights and low-heeled shoes match this dress.

But in Polish, starting with Do tej sukienki helps set the topic first: as for this dress...

Then pasują comes next, and the things that match are named after it.

So this word order sounds natural and often slightly emphasizes the dress first:

• Do tej sukienki pasują czarne rajstopy i buty na niskim obcasie.

You could also say:

• Czarne rajstopy i buty na niskim obcasie pasują do tej sukienki.

This means basically the same thing, but the focus feels a bit different.

It is genitive singular.

Why?

Because do takes the genitive case.

Breakdown:

• ta → nominative feminine singular
• tej → genitive feminine singular
• sukienka → nominative singular
• sukienki → genitive singular

So:

• ta sukienka = this dress
• do tej sukienki = for/to this dress, idiomatically with this dress

Because rajstopy is a plural noun, and the adjective has to agree with it.

• czarne is the plural form used with non-masculine-personal nouns
• rajstopy is plural and not masculine personal

So:

• czarne rajstopy = black tights
• czarne buty = black shoes
• czarne skarpetki = black socks

Polish adjectives must match the noun in gender, number, and case.

Here czarne rajstopy is in the nominative plural, because it is part of the subject of the sentence.

Usually yes. Rajstopy is normally treated as a plural-only noun in everyday use, similar to how some clothing words in English are often plural in meaning.

So you say:

• te rajstopy = these tights
• czarne rajstopy = black tights
• Nowe rajstopy są drogie. = New tights are expensive.

Because it behaves as plural, the verb is plural too:

• Rajstopy pasują.
• Rajstopy są wygodne.

Buty is in the nominative plural.

It is part of the subject of the sentence:

• czarne rajstopy i buty na niskim obcasie = the things that match

Since these are the things doing the matching in grammatical terms, they appear in the nominative.

The phrase na niskim obcasie describes buty.

This is a very common Polish way to describe shoes by the kind of heel they have.

• buty na obcasie = heeled shoes
• buty na wysokim obcasie = high-heeled shoes
• buty na niskim obcasie = low-heeled shoes

After na in this expression, Polish uses the locative:

• obcas → obcasie
• niski → niskim

So:

• na niskim obcasie = literally something like on a low heel, but naturally with a low heel / low-heeled

This is more idiomatic than translating word-for-word from English.

You might be understood, but na niskim obcasie is the more natural and standard phrase for shoes.

Polish commonly says:

• buty na obcasie
• sandały na obcasie
• kozaki na wysokim obcasie

So for footwear, na ... obcasie is the usual pattern.

It can mean both, depending on context.

1. match / go with / suit stylistically

   • Ta torebka pasuje do sukienki.
   • This handbag matches the dress.

2. fit in size/shape

   • Te buty mi pasują.
   • These shoes fit me.

3. suit someone

   • Ten kolor ci pasuje.
   • This color suits you.

In your sentence, the meaning is clearly the first one: to match/go with.

That is because languages organize meaning differently.

In Polish, the idea go with / match is expressed by the pattern:

• pasować do + genitive

So although do often means to, in this construction the whole phrase pasować do is best translated as:

• to match
• to go with
• to suit

So you should learn it as a chunk:

• pasować do czegoś = to go with something

not by translating do word for word every time.

Yes. Polish allows several word orders, depending on emphasis.

For example:

• Do tej sukienki pasują czarne rajstopy i buty na niskim obcasie.
• Czarne rajstopy i buty na niskim obcasie pasują do tej sukienki.
• Czarne rajstopy pasują do tej sukienki, i buty na niskim obcasie też.

The first version sounds very natural if you want to begin with the dress and then say what goes with it.

So the original sentence is not unusual at all — it is a normal, natural Polish structure.

Then the verb would also become singular.

For example:

• Do tej sukienki pasuje czarna torebka.
• A black handbag matches this dress.

Compare:

• pasuje = singular
• pasują = plural

So the form of pasować changes depending on whether the matching item is singular or plural.