Na stadionie wszyscy kibicujemy tej drużynie.

Polish usually says na stadionie for at the stadium / in the stadium. With places like stadion, boisko, or lotnisko, Polish often uses na where English might use in or at.

Here, na stadionie means at the stadium or in the stadium context.

Also, after na in this meaning, stadion takes the locative case:

• stadion → na stadionie

So:

• na stadionie = at/in the stadium

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

In this sentence, it refers to people, so Polish uses wszyscy.

Compare:

• wszyscy = everyone / all people
• wszystko = everything

So you say:

• wszyscy kibicujemy = we all support/cheer for not
• wszystko kibicujemy, because that would use the form for things, not people

Because the sentence includes the speaker as part of the group.

Kibicujemy is the 1st person plural form of kibicować, meaning we support / we cheer for.

The sentence is not just saying that people in general support the team. It means we all support this team at the stadium.

A quick breakdown:

• kibicuję = I support / I cheer
• kibicujesz = you support
• kibicuje = he/she/it supports
• kibicujemy = we support
• kibicujecie = you all support
• kibicują = they support

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

So Polish says literally something like:

• to support/cheer to a team

That is why:

• ta drużyna = this team becomes
• tej drużynie = to/for this team

Compare the cases:

• nominative: ta drużyna
• accusative: tę drużynę
• dative: tej drużynie

Since kibicować requires the dative, the correct phrase is:

• kibicować tej drużynie

It can mean both, depending on context.

In sports contexts, kibicować often means:

• to cheer for
• to root for
• to support

In this sentence, because we are na stadionie, it may feel especially close to cheer for, but support is also a good translation.

Related words:

• kibic = fan, supporter
• kibicować komuś/czemuś = to support / root for someone or something

Stadionie is in the locative case.

The basic form is:

• stadion

After the preposition na when talking about location, Polish uses the locative:

• na stadionie = at/in the stadium

So:

• nominative: stadion
• locative: na stadionie

This is a very common pattern:

• na stole = on the table
• na uniwersytecie = at the university
• na stadionie = at the stadium

Yes. Polish word order is fairly flexible, although the neutral order here is very natural:

• Na stadionie wszyscy kibicujemy tej drużynie.

Other possible orders include:

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

The meaning stays similar, but the emphasis changes:

• Na stadionie first emphasizes the place
• wszyscy first emphasizes that everyone is doing it
• tej drużynie first emphasizes which team

So the original sentence sounds natural and balanced, especially if the speaker wants to set the scene first: At the stadium, we all support this team.

Because tej is the form of ten/ta/to needed for the dative case and for a feminine noun.

The noun drużyna is feminine, so:

• nominative: ta drużyna = this team
• dative: tej drużynie = to/for this team

Both words change:

• ta → tej
• drużyna → drużynie

This is very common in Polish: the demonstrative word and the noun both reflect the required case.

In this sentence, it most naturally means all of us or we all, because the verb is kibicujemy = we support.

So although wszyscy by itself can often be translated as everyone, the full phrase here is really:

• we all support this team

If the verb were different, the meaning might shift:

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

Yes. Drużyna is a feminine noun.

You can tell partly from the -a ending, which often marks feminine nouns in Polish. Because it is feminine, other words agreeing with it must use feminine forms:

• ta drużyna
• tej drużynie

This matters for adjectives and pronouns too:

• nasza drużyna = our team
• tej dobrej drużynie = to/for this good team

Yes. Those are good alternatives, but the grammar changes depending on the noun.

Examples:

• kibicujemy tej drużynie = we support this team
• kibicujemy tej ekipie = we support this squad/team
• kibicujemy temu zespołowi = we support this team/group

Why the forms differ:

• drużyna is feminine → tej drużynie
• ekipa is feminine → tej ekipie
• zespół is masculine → temu zespołowi

So the key idea stays the same: kibicować requires the dative case.