Ta szara spódnica pasuje do białej bluzki.

Because spódnica (skirt) is a feminine noun in Polish.

Polish demonstratives change for gender:

• ten = masculine
• ta = feminine
• to = neuter

So:

• ta spódnica = this skirt

Since spódnica is feminine, both the demonstrative and the adjective must match it:

• ta szara spódnica

Szara is the feminine singular form of the adjective szary (gray).

Adjectives in Polish must agree with the noun in:

• gender
• number
• case

Because spódnica is:

• feminine
• singular
• nominative

the adjective also takes the feminine singular nominative form:

• szary → masculine
• szara → feminine
• szare → neuter

So:

• ta szara spódnica = this gray skirt

Because after do, the noun usually goes into the genitive case.

The basic form is:

• biała bluzka = a white blouse / the white blouse

But in this sentence, we have:

• do białej bluzki

That is the genitive singular form of both the adjective and the noun.

So the pattern is:

• nominative: biała bluzka
• genitive: białej bluzki

This happens because pasować do means to go well with / to match, and do requires the genitive.

Pasować do means to match, to suit, or to go well with.

In clothing contexts, it often means that one item looks good with another:

• Ta spódnica pasuje do tej bluzki. = This skirt matches this blouse.

It is a fixed pattern:

• pasować do + genitive

So you do not say just pasuje białą bluzkę.
You say:

• pasuje do białej bluzki

Because spódnica is the subject of the sentence, while bluzki is part of the phrase after do.

In this sentence:

• Ta szara spódnica = the thing doing the matching, so it is the subject
• subjects normally appear in the nominative
• do białej bluzki is a prepositional phrase, and do requires the genitive

So:

• spódnica stays nominative
• bluzka changes to genitive: bluzki

Yes. Pasuje is the 3rd person singular form of pasować.

The subject is:

• ta szara spódnica = this gray skirt

That subject is singular, so the verb is singular:

• pasuje = it matches / it suits

If the subject were plural, the verb would change:

• Te szare spódnice pasują do białej bluzki. = These gray skirts match the white blouse.

Yes. Polish word order is more flexible than English word order because endings show grammatical relationships.

The neutral, natural order here is:

• Ta szara spódnica pasuje do białej bluzki.

But other orders are possible, especially for emphasis, for example:

• Do białej bluzki pasuje ta szara spódnica. = emphasis on with the white blouse

• Ta szara spódnica do białej bluzki pasuje. = more marked, stylistic, or contrastive

Even though these versions are possible, the original sentence is the most natural choice for a learner.

Because it is the feminine singular genitive form of the adjective biały (white).

Here are the relevant forms:

• nominative feminine: biała
• genitive feminine: białej

Since bluzka is feminine, and since do requires the genitive, the adjective must also be feminine genitive:

• do białej bluzki

This is normal adjective agreement in Polish.

It is singular here.

That can be confusing, because bluzki can also be a plural nominative/accusative form in other contexts.

But in this sentence, bluzki is:

• genitive singular of bluzka

You can tell from the phrase:

• do białej bluzki

Both words are feminine singular genitive:

• białej
• bluzki

So the meaning is:

• to/with a white blouse not
• to/with white blouses

You can, but it does not mean exactly the same thing.

• pasuje do = matches / goes well with
• jest dobra do = is good for / suitable for

For clothing combinations, pasuje do is the most natural and idiomatic choice.

So:

• Ta szara spódnica pasuje do białej bluzki. sounds natural for talking about matching clothes.

Polish often does not use articles like the or a, because Polish has no articles.

So the same sentence can often mean either:

• This gray skirt matches a white blouse
• This gray skirt matches the white blouse

If you want to remove the sense of this, you can say:

• Szara spódnica pasuje do białej bluzki.

That can mean:

• The gray skirt matches the white blouse
• A gray skirt matches a white blouse

Context usually makes it clear.

A rough English-friendly pronunciation is:

• spódnica ≈ spoOD-nee-tsa
• bluzki ≈ BLOO-skee
• pasuje ≈ pa-SOO-yeh

A few useful notes:

• ó sounds like Polish u
• c sounds like ts
• j sounds like English y

So:

• białej bluzki is roughly BYA-wej BLOO-skee

The exact Polish sounds are a bit different from English, but that approximation is a good start.