Learn Hardcore Indonesian: Tim kami menang dalam kompetisi itu.

In Indonesian, the possessed noun usually comes first and the owner comes after it. So you say tim kami literally team we (our).
Putting kami first (kami tim) is ungrammatical in this meaning. This same pattern appears in phrases like rumah saya (my house), mobil mereka (their car), guru kita (our teacher).

What is the difference between kami and kita? Could this sentence use kita?

Both kami and kita mean we / us / our, but:

kami = we (excluding the person you’re talking to)
kita = we (including the person you’re talking to)

So tim kami means our team (but not including you), while tim kita means our team (including you).
Grammatically you could say Tim kita menang dalam kompetisi itu, but it changes the nuance: it includes the listener as part of the team or group behind it.

Can I drop kami and just say Tim menang dalam kompetisi itu?

Yes, but the meaning changes.

Tim kami menang… = Our team won…
Tim menang… = The team won… (no information about whose team it is).

So dropping kami is fine grammatically, but you lose the possessive our.

How do we know that menang here means won (past) and not wins or will win?

Indonesian verbs like menang do not change form for tense. The time (past, present, future) is understood from context or from extra words like kemarin (yesterday), tadi (earlier), nanti (later), akan (will).
So Tim kami menang dalam kompetisi itu could mean Our team won / wins / is winning / will win in that competition, depending on context. If you want to make the past clear, you might say Tim kami menang dalam kompetisi itu kemarin.

Why is dalam used here? Can I say di kompetisi itu or just Tim kami menang kompetisi itu?

Dalam literally means in / inside, and here it works like in (the context of) that competition. You can also say:

Tim kami menang di kompetisi itu – very common in speech; di is more general (at / in).
Tim kami menang kompetisi itu – also possible; here kompetisi itu is treated as the direct object: Our team won that competition.

All three are understandable. Menang kompetisi itu sounds a bit more compact and is close to the English structure win a competition.

What’s the difference between menang and memenangkan?

Menang is intransitive: to win, with focus on the winner.

Tim kami menang. = Our team won.

Memenangkan is transitive: to win (something).

Tim kami memenangkan kompetisi itu. = Our team won that competition.

In this sentence, using menang dalam kompetisi itu or memenangkan kompetisi itu are both natural; the latter sounds a bit more formal and direct.

What exactly does itu mean in kompetisi itu? Is it that competition or the competition?

Itu literally means that, but very often it works like the for a specific, known thing. Kompetisi itu is that competition in a literal translation, but in many contexts it’s perfectly natural to translate it as the competition in English.
It implies that both speaker and listener know which competition is being referred to (already mentioned, or obvious from context).

Can itu be put before the noun, like itu kompetisi?

In standard Indonesian, the normal order is noun + itu, so kompetisi itu.
Itu kompetisi is possible but has a different structure and feel; it’s more like That is a competition or a special emphasis pattern, not just that competition as a noun phrase. For simple that competition / the competition, stick to kompetisi itu.

Is kompetisi the only word for competition? What about lomba?

Both kompetisi and lomba can mean competition, but there is a nuance:

Kompetisi is a direct loan from English competition, often used in more formal, professional, or sports contexts.
Lomba is very common for contests, school competitions, small-scale events, and feels a bit more everyday and informal.

You could say Tim kami menang dalam lomba itu, depending on the type of event and tone you want.

Can I change the word order to put the competition first, like Dalam kompetisi itu, tim kami menang?

Yes, that’s perfectly natural. Dalam kompetisi itu, tim kami menang means the same thing, just with a different emphasis.
Starting with Dalam kompetisi itu highlights the competition context first (like English In that competition, our team won), which is common in narration or writing.

Is this sentence formal or informal? In what situations can I use it?

Tim kami menang dalam kompetisi itu is neutral and can be used in both spoken and written Indonesian. It’s fine in casual conversation, in the news, in a school report, or in a simple written summary.
If you needed something very formal (e.g., a written report), you might slightly expand it or vary the verb (memenangkan), but the sentence as given is already acceptable in most contexts.