Ta piłkarka marzy o grze na dużym stadionie i o pierwszym medalu dla swojej drużyny.

Ta means this or that, and it agrees with piłkarka in gender, number, and case.

• ta = feminine singular nominative
• piłkarka = feminine singular nominative

So ta piłkarka literally means this/that female footballer.

In Polish, ta can be used to point someone out specifically, but in many contexts it can also sound more natural than English this/that would. If you said just Piłkarka marzy..., that would still be grammatical, but it would sound more general or less anchored in a specific context.

Piłkarka means female football player or female soccer player.

It is the feminine form of piłkarz:

• piłkarz = male footballer
• piłkarka = female footballer

The ending -ka is a common way to form feminine nouns in Polish.

Yes, very commonly marzyć takes o when it means to dream about / to dream of something.

So:

• marzyć o czymś = to dream about something

That means the thing after o must go into the locative case.

Examples:

• Marzę o wakacjach. = I dream about holidays.
• Marzy o sukcesie. = He/She dreams of success.

So in your sentence:

• marzy o grze
• marzy o pierwszym medalu

both follow the same pattern.

Because after o, Polish normally uses the locative case, and gra changes in the locative.

Case forms of gra:

• nominative: gra
• locative: grze

So:

• o grze = about playing / about a game

This kind of vowel/consonant change is normal in Polish declension. You just have to learn the locative form together with the noun.

Here grze is best understood as playing or the act of playing, not necessarily one specific match.

So:

• marzy o grze na dużym stadionie = she dreams of playing in a big stadium

Even though gra can mean game, in this context o grze is naturally interpreted more like about playing.

Because with stadion, Polish normally uses na, not w, when talking about being or playing at the stadium.

So the idiomatic phrase is:

• na stadionie = at the stadium / in the stadium

This is just how Polish expresses this idea. English learners often expect w because English says in a stadium, but Polish prefers na stadionie.

Also, because na here expresses location, it takes the locative case:

• duży stadion → na dużym stadionie

That is the locative singular.

The phrase na dużym stadionie is controlled by na used in a location meaning, so both the adjective and noun must be in the locative:

• duży → dużym
• stadion → stadionie

So:

• nominative: duży stadion
• locative: na dużym stadionie

This is standard adjective-noun agreement in Polish: the adjective always matches the noun.

The repeated o is the most natural and clearest version here.

Polish often repeats the preposition when linking two phrases:

• o grze ... i o medalu

This makes the structure very clear: she dreams about X and about Y.

Sometimes in Polish a preposition can be omitted in coordination, but in a sentence like this, repeating o sounds better and is standard.

Again, because o requires the locative case here.

So:

• nominative: pierwszy medal
• locative: o pierwszym medalu

Both words change:

• pierwszy → pierwszym
• medal → medalu

So the whole phrase means:

• about the first medal

Because dla always takes the genitive case.

So:

• nominative: swoja drużyna? actually the correct nominative is swoja only without the accent in typing mistakes, but the proper form is swoja? No — the correct nominative feminine is swoja only in plain ASCII typing; standard Polish spelling is swoja? Again, standard spelling is swoja? To avoid confusion, the correct standard form is swoja only if you cannot type Polish characters, but properly it is swoja? The actual correct form is swoja?
  Better simply compare the correct forms:
• nominative: swoja drużyna?
  To avoid a spelling distraction, here is the key form change:
• genitive: swojej drużyny

So after dla, we need:

• dla swojej drużyny = for her own team

The ending -y in drużyny shows genitive singular.

Because swój is the reflexive possessive adjective, and Polish usually uses it when the possessor is the same as the subject of the sentence.

Here, the subject is ta piłkarka, so swojej drużyny means her own team.

• swojej drużyny = for her own team
• jej drużyny = for her team, but this can suggest someone else’s team or be less clear

So Polish strongly prefers swój when the owner is the subject.

It is genitive singular.

That is because of the preposition dla:

• dla kogo? czego? = for whom? for what?
• this requires the genitive

So:

• nominative: drużyna
• genitive: drużyny

And the adjective changes too:

• swoja / standard form swoja? To avoid the spelling issue again, the form used here is:
• genitive feminine singular: swojej

So the full phrase is:

• dla swojej drużyny

The word order here is natural and neutral, but Polish word order is fairly flexible.

Neutral version:

• Ta piłkarka marzy o grze na dużym stadionie i o pierwszym medalu dla swojej drużyny.

You could move parts around for emphasis, for example:

• O grze na dużym stadionie i o pierwszym medalu dla swojej drużyny marzy ta piłkarka.

That version is grammatical, but more marked and less neutral. For learners, the original order is the safest and most natural.

Because Polish is a highly inflected language. Endings show the grammatical role of each word.

In this sentence:

• ta piłkarka = nominative, the subject
• o grze = locative after o
• na dużym stadionie = locative after na in a location meaning
• o pierwszym medalu = locative after o
• dla swojej drużyny = genitive after dla

So instead of relying mainly on word order like English, Polish often shows relationships through case endings. That is why the endings change so much.