Learn Hardcore Indonesian: Kami berkemas di rumah sebelum berlibur ke pulau kecil itu. - We pack at home before vacationing to that small island.

In Kami berkemas di rumah…, the sentence implies the listener is not part of the group that is packing and going on vacation.
If the speaker wanted to include the listener in the trip, they would say:

Kita berkemas di rumah sebelum berlibur ke pulau kecil itu.
= We (you and I) pack at home before going on vacation to that small island.

What does the prefix ber- in berkemas mean? Is kemas a word by itself?

The prefix ber- often makes an intransitive verb (an action without a direct object).

kemas as a root has the idea of neat, tidy, orderly.
berkemas means to get things ready / to pack (for a trip), literally “to make oneself ready with one’s things.”

Compare:

Dia sedang berkemas. = He/She is packing / getting ready.
Dia mengemas kopernya. = He/She is packing his/her suitcase.

So:

berkemas = the general activity of packing/getting ready (no direct object needed).
mengemas = to pack something specific (takes a direct object).

Why doesn’t berkemas have an object, like “pack our bags”?

Because berkemas is normally used without a direct object. It already means “to pack (one’s things)” in a general sense.

In Indonesian you usually say:

Kami berkemas di rumah. = We pack (our things) at home.

If you want to mention exactly what you pack, you usually switch to mengemas:

Kami mengemas koper kami di rumah.
= We pack our suitcases at home.
Dia mengemas pakaian di kamar.
= He/She packs clothes in the room.

Saying berkemas koper is not natural; speakers expect mengemas koper or just berkemas without an object.

Why do we need di before rumah? Can we say Kami berkemas rumah?

You need di because Indonesian usually marks locations with a preposition:

di = at / in / on (static location)
ke = to / towards (movement)

So:

Kami berkemas di rumah.
= We pack at home.

Kami berkemas rumah is ungrammatical in standard Indonesian.
You almost always say di rumah, di kantor, di hotel, etc., for locations where something happens.

Can we change the word order to Kami di rumah berkemas sebelum…?

Yes, Kami di rumah berkemas sebelum berlibur… is grammatically possible, but the nuance changes slightly.

Kami berkemas di rumah sebelum…
→ Neutral, most natural order. Focus is on the action berkemas; di rumah just tells you where.
Kami di rumah berkemas sebelum…
→ Puts more emphasis on the location di rumah (“we, at home, are packing…”). It can sound slightly more marked or stylistic.

In everyday speech and writing, the original Kami berkemas di rumah… is the more typical word order.

What exactly does sebelum do in this sentence?

Sebelum means before and introduces a time clause: something that happens earlier than something else.

In Kami berkemas di rumah sebelum berlibur ke pulau kecil itu:

Main action: Kami berkemas di rumah (We pack at home)
Time clause: sebelum berlibur ke pulau kecil itu (before going on vacation to that small island)

So the structure is:
[Main clause] + sebelum + [what happens afterward].

Why is it sebelum berlibur and not sebelum kami berlibur?

Both are possible:

sebelum berlibur ke pulau kecil itu
sebelum kami berlibur ke pulau kecil itu

Indonesian often omits the subject in the second clause when it is the same as in the first clause.
Here, the subject in both clauses is kami, so the second kami can be dropped:

Kami berkemas di rumah sebelum (kami) berlibur ke pulau kecil itu.

Adding kami makes the subject explicit but is not required. The version without it sounds a bit smoother and is very common.

What is the difference between berlibur and liburan?

berlibur = to go on vacation / to be on vacation (verb)
liburan = vacation / holiday (noun), and also used colloquially as a verb

Standard / careful Indonesian prefers:

Kami akan berlibur ke pulau kecil itu.
= We will go on vacation to that small island.

But in everyday speech you might hear:

Kami liburan ke pulau kecil itu.
= (Colloquial) We go/went on vacation to that small island.

In your sentence, berlibur is the standard verb form, which is why it’s used.

Why is it berlibur ke pulau kecil itu and not berlibur di pulau kecil itu?

ke and di show slightly different ideas:

ke = to (destination / direction)
di = at / in (location where something happens)

So:

berlibur ke pulau kecil itu
= go on vacation to that small island (focus on going there as the destination).
berlibur di pulau kecil itu
= be on vacation on that small island (focus on spending the vacation there).

Your sentence talks about packing before going there, so ke (destination) is the natural choice.

How is pulau kecil itu structured? Why is itu at the end?

The phrase pulau kecil itu follows normal Indonesian noun phrase order:

pulau = island (main noun)
kecil = small (adjective comes after the noun)
itu = that (demonstrative comes at the very end of the phrase)

So pulau kecil itu literally = island small that, but in English word order: that small island.

You generally don’t say itu pulau kecil to mean that small island; itu pulau kecil is more like a full clause: That is a small island.
Within a noun phrase, the normal pattern is Noun + Adjective + ini/itu.

What exactly does itu add to pulau kecil itu? Is it like “the small island”?

itu literally means that, but it also has a broader function:

It can mean that (physically far or not near the speaker/listener).
It can refer to something already known or mentioned in the conversation.
It often behaves like English the when both sides know which thing is meant.

So:

pulau kecil itu
= that small island / the small island (we both know which one)

Without itu:

pulau kecil
= a small island / small islands (more general, not a specific one already known in the context).

Does this sentence show past or future tense, or could it be either?

Indonesian verbs do not change form for tense. Berkemas and berlibur stay the same for past, present, and future.

The sentence Kami berkemas di rumah sebelum berlibur ke pulau kecil itu could mean:

We packed at home before going on vacation…
We are packing at home before going on vacation…
We will pack at home before going on vacation…

To make the time clearer, Indonesians add time words:

Tadi kami berkemas di rumah sebelum berlibur…
= Earlier we packed at home before going…
Besok kami akan berkemas di rumah sebelum berlibur…
= Tomorrow we will pack at home before going…

Is berlibur ke pulau kecil itu the same as pergi ke pulau kecil itu untuk berlibur?

They are very close in meaning, but not identical in structure:

berlibur ke pulau kecil itu
= go on vacation to that small island (the idea of “go” and “vacation” is bundled into one verb: berlibur).
pergi ke pulau kecil itu untuk berlibur
= go to that small island in order to have a vacation (explicitly: go
- to
  - for vacation).

In practice, they usually describe the same situation.
Your sentence uses the more compact form with berlibur ke…, which is very natural and idiomatic.