Na stadionie wszyscy kibicujemy tej drużynie.

Because na stadionie is in the locative case, used after na when it means in/on/at a location.

• na stadionie = at the stadium
• na stadion would suggest movement toward the stadium in some contexts, but with stadion you would more naturally say na stadion only in certain directional uses, while here the sentence is describing where something is happening, not motion.

So:

• Jesteśmy na stadionie. = We are at the stadium.
• Idziemy na stadion. = We are going to the stadium.

Because after na in a location meaning, Polish usually uses the locative case.

The noun stadion is a masculine noun, and in the locative singular it becomes:

• stadion → stadionie

This -ie ending is very common in the locative singular for many nouns.

Wszyscy means everyone or all of us / all people depending on context.

In this sentence it refers to the people included in we support, so it has the sense of we all.

It is in the masculine personal plural form because Polish uses that form when referring to a mixed group of people or a group of people in general.

Compare:

• wszyscy = all/everyone, for groups including people
• wszystkie = all, for non-masculine-personal plural groups

Here, since we are talking about people at the stadium, wszyscy is the correct form.

In Polish, the verb ending usually already shows the subject, so you often do not need to say my for we.

• kibicuję = I support / I cheer for
• kibicujesz = you support
• kibicujemy = we support

So kibicujemy already means we support / we cheer for.

You could say my kibicujemy, but that adds emphasis, something like we are the ones who support.

It is present tense, first person plural.

From the verb:

• kibicować = to support / to cheer for

Conjugation:

• ja kibicuję
• ty kibicujesz
• on/ona kibicuje
• my kibicujemy
• wy kibicujecie
• oni/one kibicują

So kibicujemy = we support / we are cheering for.

In Polish, the present tense of an imperfective verb can also sometimes match English are cheering depending on context.

Because the verb kibicować takes the dative case, not the accusative.

So Polish says, literally:

• kibicować komu? czemu? = to support / cheer for to whom? to what?

That is why:

• ta drużyna = this team
• tej drużynie = to this team

If the verb required the accusative, you might expect tę drużynę, but kibicować does not work that way.

This is one of the most important things to remember in the sentence: kibicować + dative

Both words are in the dative singular feminine.

The basic noun is:

• drużyna = team

Its dative singular form is:

• drużynie

The demonstrative adjective changes with it:

• ta drużyna = this team
• tej drużynie = to this team

So the adjective and noun must match in:

• gender
• number
• case

That is why both words change together.

The dictionary form is drużyna.

Here are the relevant forms:

• drużyna = nominative singular
• drużynie = dative singular
• drużynę = accusative singular

That helps show why tej drużynie is not the same as tę drużynę.

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

The neutral sentence is:

• Na stadionie wszyscy kibicujemy tej drużynie.

But you could also say:

• Wszyscy kibicujemy tej drużynie na stadionie.
• Tej drużynie wszyscy kibicujemy na stadionie.

These versions are all understandable, but the emphasis changes.

For example:

• Na stadionie first emphasizes the location.
• Wszyscy first emphasizes that everybody is doing it.
• Tej drużynie first emphasizes which team.

So the original sentence feels like: At the stadium, we all support this team.

Not exactly.

• kibicować = to cheer for, root for, support in a sports or competition sense
• lubić = to like
• popierać = to support in a broader sense, often opinions, plans, political ideas, or causes

So with a sports team, kibicować is the natural verb.

Examples:

• Kibicuję tej drużynie. = I support / root for this team.
• Lubię tę drużynę. = I like this team.
• Popieram tę decyzję. = I support this decision.

In this sentence, because the verb is kibicujemy = we support, the natural meaning is we all.

But literally wszyscy can often be translated as everyone depending on the structure.

So:

• Wszyscy kibicujemy tej drużynie. = We all support this team.
• Wszyscy kibicują tej drużynie. = Everyone supports this team.

The verb form tells you which meaning fits.

In many contexts, ten / ta / to can correspond to either this or that in English, depending on how specific or immediate the reference feels.

So:

• tej drużynie can be translated as this team
• but in another context it might feel closer to that team

Polish does not always make the same strict this/that distinction that English does in everyday use.

A rough English-friendly guide is:

• kee-bee-tsoo-YEH-my

A few helpful notes:

• ki sounds like kee
• bi sounds like bee
• cu in -cuj- gives a ts sound: tsoo
• the stress is usually on the second-to-last syllable, so: ki-bi-cu-JE-my

Polish spelling is fairly regular, so once you learn the sound patterns, words like this become easier to read.