Learn Hardcore Indonesian: Keluarga kami berkumpul di ruang tamu untuk memperingati hari kemerdekaan. - Our family gathers in the living room to commemorate Independence Day.

Kami keluarga is not a natural way to say our family.
Kami on its own is the subject pronoun we, not a possessive adjective like our in English.

What is the difference between keluarga kami and keluarga kita?

Both can be translated as our family, but:

kami = we/us (excluding the listener)
kita = we/us (including the listener)

So:

keluarga kami: our family, but your family is not included
- e.g. my family and I are gathering; you are an outsider.
keluarga kita: our family, including the listener
- e.g. you are also part of this family.

In the sentence, keluarga kami implies the speaker is talking about their own family to someone who is not part of that family.

What exactly does berkumpul mean, and how is it different from kumpul or mengumpulkan?

kumpul is the basic root meaning to gather / to get together (informal).
berkumpul = to gather, to assemble (intransitive, a group comes together by itself)
mengumpulkan = to gather/collect something (transitive, you gather objects or people)

Examples:

Keluarga kami berkumpul di ruang tamu.
Our family gathers in the living room. (they come together themselves)
Dia mengumpulkan koin.
He/She collects coins. (he actively gathers coins)

In spoken, informal Indonesian you might also hear:

Keluarga kami kumpul di ruang tamu. (dropping ber-)

How does di work in di ruang tamu? Why not ke ruang tamu?

di and ke are both common prepositions, but they are different:

di = at / in / on (location, where something is)
ke = to / toward (direction, where something is going)

In the sentence:

di ruang tamu = in the living room (location of the gathering)

If you talked about movement to the living room, you would use ke:

Kami pergi ke ruang tamu.
We went to the living room.

Does ruang tamu mean “living room” or “guest room”? Is there any cultural nuance?

Literally, ruang tamu is:

ruang = room/space
tamu = guest

So it is literally guest room, but in everyday use it usually corresponds to the living room / sitting room, that front room where:

you receive guests,
the family often sits together,
there may be a TV, sofa, etc.

In some houses there might be:

ruang tamu (front area for guests) and
ruang keluarga (more private family room),

but often ruang tamu is simply used as living room in practice.

What does untuk mean here in untuk memperingati hari kemerdekaan, and could we leave it out?

untuk most often means:

for, to, or in order to (expressing purpose)

In the sentence:

berkumpul ... untuk memperingati hari kemerdekaan
= gathered to commemorate Independence Day
= gathered in order to commemorate Independence Day

You can often omit untuk before a verb of purpose, especially in less formal language:

Keluarga kami berkumpul di ruang tamu memperingati hari kemerdekaan.

This is still understandable and natural in speech, but the version with untuk is clearer and sounds more standard.

What exactly does memperingati mean, and when is it used?

memperingati means to commemorate / to observe (an event, day, anniversary). It’s often used in formal or semi-formal contexts:

memperingati hari kemerdekaan – to commemorate Independence Day
memperingati ulang tahun sekolah – to commemorate the school’s anniversary
memperingati hari pahlawan – to commemorate Heroes’ Day

Morphologically:

peringatan = a remembrance / warning / commemoration
memperingati = to commemorate / to observe

It is not used for casual daily remembering like remember your keys. For that you would normally use ingat or mengingat:

Ingat bawa kunci! – Remember to bring the keys!

Why is it hari kemerdekaan and not just kemerdekaan?

hari means day, so:

kemerdekaan = independence (the state/idea of being independent)
hari kemerdekaan = Independence Day

In Indonesian, many holidays and commemorative days are formed with hari + noun:

Hari Kemerdekaan – Independence Day
Hari Ibu – Mother’s Day
Hari Natal – Christmas Day

In everyday talk, people may sometimes shorten it if the context is clear:

Kami merayakan kemerdekaan.
We celebrate independence.

But if you specifically mean the calendar day, hari kemerdekaan (or capitalized Hari Kemerdekaan as a proper name) is the normal form.

What is the difference between merdeka and kemerdekaan?

merdeka is an adjective meaning free / independent.
- Negara itu merdeka. – That country is independent.
kemerdekaan is a noun meaning freedom / independence (the concept, state, or status).
- Mereka berjuang untuk kemerdekaan. – They fought for independence.

So in:

hari kemerdekaan → literally day (of) independence, not day free.

Why is there no past tense marker in the Indonesian sentence, even though the English translation is in the past?

Indonesian verbs usually do not change form for tense (past / present / future). Time is understood from:

context,
time expressions (kemarin, besok, tadi),
or optional markers like sudah (already), akan (will).

So the same sentence can be:

past: Our family gathered in the living room…
present: Our family is gathering in the living room…
future (with a marker):
- Keluarga kami akan berkumpul di ruang tamu…
  Our family will gather in the living room…

Your original sentence is understood as past because of context (e.g. part of a narrative), not because of verb endings.

Can we omit kami and just say Keluarga berkumpul di ruang tamu untuk memperingati hari kemerdekaan?

Yes, grammatically that is fine:

Keluarga berkumpul di ruang tamu ...
= The family gathered in the living room...

However, the nuance changes:

keluarga kami = our family (specifically, belonging to the speaker)
keluarga (without a pronoun) = the family (more general, could be any family, or context decides which one)

If you want to be clear it’s your own family, keeping kami is better.

Is di ruang tamu enough, or should it be di ruang tamu kami to say “in our living room”?

Both are possible:

di ruang tamu – in the living room (context usually makes it clear whose)
di ruang tamu kami – in our living room (explicitly our family’s living room)

In many real-life situations:

If you already said keluarga kami and there is no other location involved, listeners will naturally assume di ruang tamu refers to your living room.
Adding kami is only needed if there might be ambiguity.

What is the register (formality level) of memperingati hari kemerdekaan? Is it formal?

Yes, memperingati hari kemerdekaan sounds formal or semi-formal, typical of:

news reports,
official speeches,
written texts (essays, reports, school books).

In everyday casual speech, people might say:

merayakan hari kemerdekaan – to celebrate Independence Day
ngumpul buat 17-an – get together for Independence Day activities (very informal; 17-an refers to 17 August in Indonesia)

How do you pronounce kemerdekaan and where is the stress?

kemerdekaan is divided as:

ke-mer-de-ka-an

Pronunciation tips:

ke – like ke in ketchup, but shorter and more neutral
mer – mer as in mercy (but without the English “r” coloring; Indonesian r is tapped)
de – like de in deny
ka – like ka in karaoke
an – an as in fun, but n is clearly pronounced

Stress in Indonesian is usually light and often falls near the second-to-last syllable, so you can say it as:

ke-MER-de-KA-an

with a slightly stronger beat on MER and KA, but not as strong or contrastive as English stress. The main thing is to pronounce all syllables clearly.