Learn Hardcore Indonesian: Kadang-kadang saya belajar sendiri di perpustakaan. - Sometimes I study by myself in the library.

Repeating the word (kadang-kadang) sounds more natural and is the standard way to say sometimes.
Kadang by itself is also used in everyday speech, but feels a bit shorter/more casual.

So:

Kadang-kadang saya belajar sendiri di perpustakaan. = Natural, standard.
Kadang saya belajar sendiri di perpustakaan. = Also okay, a bit more casual.

Why is there a hyphen in kadang-kadang? Can I write it without the hyphen?

The hyphen shows that it’s a reduplication (word repeated to form a new meaning).

Correct formal writing: kadang-kadang
In informal text (chat, SMS), you might see kadang kadang (with a space) or even kadangkadang, but these are not standard.

For proper Indonesian, especially in learning and writing, use kadang-kadang.

Can I move kadang-kadang to another place in the sentence, like Saya kadang-kadang belajar sendiri di perpustakaan?

Yes. Word order is quite flexible for adverbs of time:

Kadang-kadang saya belajar sendiri di perpustakaan.
Saya kadang-kadang belajar sendiri di perpustakaan.

Both are correct and natural.
Placing kadang-kadang at the beginning sounds slightly more emphatic or “topic-like” (As for sometimes, I study on my own at the library), but in everyday speech the difference is small.

Why is saya used here instead of aku? What’s the difference?

Both mean I / me, but differ in formality and context:

saya
- Neutral–polite, safe in almost all situations.
- Used with strangers, older people, formal contexts, writing.
aku
- Informal, used with friends, family, people of the same age or younger.

You could say:

Kadang-kadang aku belajar sendiri di perpustakaan. (informal)
Kadang-kadang saya belajar sendiri di perpustakaan. (neutral/polite)

The original sentence is neutral and polite because it uses saya.

Does belajar mean “to study” or “to learn”? Is there a tense like “I studied / I am studying”?

Belajar covers both to study and to learn depending on context.

Indonesian verbs don’t change form for tense. So belajar can mean:

study / studies / am studying / was studying / will study
learn / learns / am learning, etc.

Time is understood from context or added words:

Kemarin saya belajar sendiri di perpustakaan. = Yesterday I studied / was studying…
Sekarang saya belajar sendiri di perpustakaan. = Now I am studying…
Nanti saya belajar sendiri di perpustakaan. = Later I will study…

The original sentence is timeless by itself; English translation depends on context.

What’s the difference between belajar and mengajar?

belajar = to study / to learn (the student’s action)
mengajar = to teach (the teacher’s action)

Examples:

Saya belajar Bahasa Indonesia. = I study / I am learning Indonesian.
Dia mengajar Bahasa Indonesia. = He/She teaches Indonesian.

In the sentence, belajar sendiri implies studying/learning by oneself.

What does sendiri mean here? Does it mean “alone” or “myself”? How is it different from saya sendiri?

Sendiri can mean both alone and oneself, depending on position and context.

In the sentence:

saya belajar sendiri ≈ I study by myself / I study alone.

Contrast:

Saya belajar sendiri di perpustakaan.
- Focus: the studying is done without help / alone.
Saya sendiri belajar di perpustakaan.
- Focus: I myself (not someone else) am the one who studies at the library.
- Here sendiri emphasizes the subject (myself).

So:

[verb] sendiri → by oneself / alone
[subject] sendiri [verb] → that person himself/herself

What’s the difference between sendiri and sendirian (e.g. saya belajar sendirian)?

Both are related, but:

sendiri after a verb often means by oneself, independently, or without help.
sendirian emphasizes being physically alone, with no one else present.

Compare:

Saya belajar sendiri di perpustakaan.
→ I study by myself (maybe still around other people, but I’m not working with them).
Saya belajar sendirian di perpustakaan.
→ I study all alone at the library (no friends with me).

In many contexts they overlap, but sendirian is stronger on the “no one else is with me” idea.

Why is it di perpustakaan and not ke perpustakaan?

di = at / in / on (location)
ke = to (movement toward a place)

So:

Saya belajar di perpustakaan. = I study at the library. (location)
Saya pergi ke perpustakaan. = I go to the library. (movement)

In the sentence, you are at the library while studying, so di is correct.

What does perpustakaan literally mean? Is there a base word?

Yes. Perpustakaan = library.

It comes from:

base word pustaka = book / written work (a bit formal/old-fashioned)
prefix–suffix per- … -an to form a place related to that thing

So per + pustaka + an = place of books → perpustakaan (library).

You usually don’t say pustaka in everyday speech; people just say perpustakaan for library.

Can I drop saya and just say Kadang-kadang belajar sendiri di perpustakaan?

Yes, in informal conversation, Indonesian often drops the subject if it’s clear from context.

Kadang-kadang belajar sendiri di perpustakaan.
= Sometimes (I) study by myself at the library.

However:

In writing, exercises, or when context is not super clear, it’s better to keep saya.
As a learner, using the subject (like saya) is safer and clearer.

Is it possible to put kadang-kadang at the end, like Saya belajar sendiri di perpustakaan kadang-kadang?

It’s possible, but it sounds less natural as a neutral sentence.

More natural options:

Kadang-kadang saya belajar sendiri di perpustakaan.
Saya kadang-kadang belajar sendiri di perpustakaan.

Putting kadang-kadang at the end might sometimes be used in speech for special emphasis or rhythm, but as a learner you should stick to beginning or after the subject.

Is this sentence formal, informal, or neutral? How would I say it casually to a friend?

Using saya makes it neutral–polite, acceptable in:

talking to teachers,
writing,
speaking to strangers or older people.

To say it more casually with friends, you might say:

Kadang-kadang aku belajar sendiri di perpustakaan.
Or even: Kadang-kadang gue belajar sendiri di perpustakaan. (Jakarta slang; gue = I)

But as a general rule, saya is a safe default unless you know the informal pronouns people use.