Ta spódnica pasuje do tej bluzki.

Because the two noun phrases are in different cases.

• ta spódnica = this skirt in the nominative case, because it is the subject of the sentence
• do tej bluzki = to/with this blouse after the preposition do, which requires the genitive case

So:

• ta is the nominative feminine singular form of this
• tej is the genitive feminine singular form of this

And the noun changes too:

• bluzka → bluzki in the genitive

Yes, do often means to, but in this expression pasować do means to match / to go with.

So you learn it as a set phrase:

• pasować do czegoś = to match something
• literally, something like to suit to or to fit with

Examples:

• Ta spódnica pasuje do tej bluzki. = This skirt goes with this blouse.
• Te buty pasują do sukienki. = These shoes go with the dress.

So in this sentence, do is part of the pattern required by pasować.

Here pasuje means matches, goes with, or suits.

The verb is pasować. It can have a few related meanings depending on context:

• pasować do = to match / go with
• pasować komuś = to fit someone or suit someone
• in some contexts, pasować can also mean to be appropriate

In your sentence:

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

Because after do, the noun must be in the genitive case.

The dictionary form is:

• bluzka = blouse

But after do, it changes:

• do bluzki = to/with the blouse

This is a normal feminine noun pattern:

• nominative: bluzka
• genitive: bluzki

The same happens with many feminine nouns ending in -a:

• sukienka → do sukienki
• kobieta → do kobiety
• książka → do książki

Because spódnica is the subject of the sentence, so it stays in the nominative case.

Compare:

• Ta spódnica pasuje... → This skirt matches...
  Here spódnica is doing the action, grammatically speaking.

But the second noun comes after do, so it has to change:

• do tej bluzki

So the sentence has:

• nominative subject: ta spódnica
• genitive after do: do tej bluzki

Yes. The verb agrees with the subject.

• spódnica is singular
• so the verb is pasuje = matches / goes with

If the subject were plural, the verb would change:

• Te spódnice pasują do tej bluzki. = These skirts go with this blouse.

So:

• pasuje = singular
• pasują = plural

Both are feminine nouns.

You can often guess this because they end in -a, though there are exceptions in Polish.

So:

• spódnica = feminine
• bluzka = feminine

That is why the demonstrative forms are feminine too:

• ta spódnica
• tej bluzki

If the nouns were masculine or neuter, the forms of this would be different.

Normally, no. For match/go with, the standard pattern is:

• pasować do + genitive

So the natural sentence is:

• Ta spódnica pasuje do tej bluzki.

Using z here would usually sound wrong for this meaning.

A learner should remember:

• pasować do czegoś = to match something

Yes, Polish word order is more flexible than English, though some orders sound more natural depending on emphasis.

The neutral order is:

• Ta spódnica pasuje do tej bluzki.

You could also say:

• Do tej bluzki pasuje ta spódnica.

This shifts the emphasis a bit toward this blouse.

Because Polish uses case endings, the grammatical roles are still clear even when the order changes.

A rough pronunciation guide:

• spódnica ≈ spood-nee-tsa
• bluzki ≈ bloos-kee

A few helpful points:

• ó sounds like u
• c sounds like ts
• dz / ci / ni-type combinations can soften sounds, but in spódnica the ni sounds like nee
• u in bluzki sounds like oo

A rough full-sentence pronunciation:

• Ta spódnica pasuje do tej bluzki
• ≈ Ta spood-nee-tsa pa-SOO-ye do tey BLOOS-kee

They are different case forms of the same word: ten / ta / to = this.

For feminine singular nouns:

• ta = nominative
• tej = genitive, dative, locative
• tę = accusative
• tą = instrumental

So with a feminine noun like bluzka:

• ta bluzka = this blouse
• do tej bluzki = of/to this blouse or, in this phrase, with this blouse
• widzę tę bluzkę = I see this blouse
• z tą bluzką = with this blouse

In your sentence, tej appears because do requires the genitive.

No.

• spódnica = skirt
• sukienka = dress

This matters because English speakers sometimes confuse clothing vocabulary when learning Polish.

So your sentence specifically means the skirt matches the blouse, not a dress.

You change the subject, the verb, and any other words that need to agree.

For example:

• Te spódnice pasują do tej bluzki.
  = These skirts go with this blouse.

Or if both are plural:

• Te spódnice pasują do tych bluzek.
  = These skirts go with these blouses.

Notice:

• ta → te in nominative plural
• tej bluzki → tych bluzek in genitive plural
• pasuje → pasują

So plural sentences involve agreement plus case.

Yes, very often.

For example:

• Ta spódnica mi pasuje. = This skirt fits me / suits me.
• Ta bluzka do mnie pasuje. = This blouse suits me.

So pasować can mean:

• match/go with
• fit
• suit

The meaning depends on the structure and context.

In your sentence, because of do tej bluzki, the meaning is clearly matches/goes with.