Learn Hardcore Indonesian: Sejarah kemerdekaan Indonesia penting bagi kami. - The history of Indonesia's independence is important to us.

Indonesian usually does not use a separate verb like is/are when linking a noun to an adjective.
The pattern is simply [subject] + [adjective].
So Sejarah kemerdekaan Indonesia penting is understood as “The history of Indonesia’s independence is important”.
You generally do not put adalah before an adjective here; Sejarah kemerdekaan Indonesia adalah penting sounds unnatural in normal usage.

What is the grammatical structure of Sejarah kemerdekaan Indonesia?

This is a chain of three nouns, with modifiers coming after the main noun:

sejarah = history (main noun)
kemerdekaan = independence (modifies sejarah: “history of independence”)
Indonesia = Indonesia (modifies kemerdekaan: “independence of Indonesia”)

So Sejarah kemerdekaan Indonesia means “the history of Indonesia’s independence” (literally: history [of] independence [of] Indonesia).
Indonesian often expresses “of” relationships just by putting nouns next to each other like this.

What does kemerdekaan mean, and how is it formed?

Kemerdekaan means independence or freedom (in the political/national sense).
It comes from the adjective merdeka (free, independent), plus the noun-forming affixes ke- … -an:

merdeka → kemerdekaan = the state or condition of being independent

It is commonly used for national independence, like kemerdekaan Indonesia = Indonesia’s independence.

Why does penting come after the long phrase instead of before, like in English?

Here, penting is not an adjective inside the noun phrase; it is the predicate of the whole sentence.
The structure is:

Subject: Sejarah kemerdekaan Indonesia
Predicate: penting bagi kami

So it’s like saying “The history of Indonesia’s independence (subject) important for us (predicate)”, which corresponds to English “… is important for us.”
When an adjective works as the predicate, it normally comes after the subject phrase in Indonesian.

What does bagi mean here, and how is it different from untuk?

Both bagi and untuk can be translated as for.
In this sentence, bagi introduces the person or group that something is important to:

penting bagi kami = important for/to us

General tendencies:

bagi is a bit more formal and is common in expressions of opinion, value, or effect (e.g. bagi saya, bagi masyarakat).
untuk is more general: purpose, recipient, “for the sake of”, etc.

Here you could also say penting untuk kami, and it would still be correct and natural.

What is the difference between kami and kita, and why is kami used?

Both kami and kita translate as we/us, but:

kami = we/us excluding the person you are talking to
kita = we/us including the person you are talking to

Using kami in penting bagi kami means “important for us (but not necessarily for you, the listener).”
If the speaker wanted to include the listener in that “we,” they would say penting bagi kita.

Could we add itu and say Sejarah kemerdekaan Indonesia itu penting bagi kami? What changes?

Yes, that is possible and natural.
Adding itu after the noun phrase makes it sound more definite and often a bit more emphatic or specific, like:

Sejarah kemerdekaan Indonesia penting bagi kami.
– Indonesian independence history (in general) is important to us.
Sejarah kemerdekaan Indonesia itu penting bagi kami.
– That Indonesian independence history (the one we know/talk about) is important to us.

In many contexts, the difference is subtle; both are correct.

Can bagi kami be moved to the beginning of the sentence?

Yes. You can say:

Bagi kami, sejarah kemerdekaan Indonesia penting.

This is still grammatical and natural.
Putting bagi kami first puts extra emphasis on “for us”, as in: “For us, the history of Indonesia’s independence is important.”
The meaning doesn’t really change; only the focus/emphasis does.

Is sejarah always “history,” or can it mean “story” too?

Sejarah primarily means history in the sense of historical events and their study.
For “story” in the sense of a tale, anecdote, or narrative, Indonesian normally uses cerita.
So sejarah kemerdekaan Indonesia clearly means “the history of Indonesia’s independence,” not just a story about it.

Can we drop Indonesia and just say Sejarah kemerdekaan penting bagi kami?

Yes, grammatically you can say Sejarah kemerdekaan penting bagi kami.
Without Indonesia, it means “The history of independence is important to us”, which sounds more general or ambiguous.
If you specifically mean Indonesia’s independence, it’s clearer to keep Indonesia: Sejarah kemerdekaan Indonesia penting bagi kami.