Learn Hardcore Indonesian: Saya mencatat alamat bioskop di buku kecil agar tidak lupa. - I write down the cinema's address in a small notebook so I don’t forget.

Mencatat literally means “to write down” or “to record,” with the idea of noting something for future reference. Menulis means “to write” in a general sense (e.g. writing an essay, a letter, a story).

Use mencatat when you jot down specific information you want to remember.
Use menulis for any kind of writing activity.

Why is it alamat bioskop and not bioskop alamat?

Indonesian noun compounds normally follow the pattern [head noun] + [modifier].

Alamat is the head noun (“address”), and bioskop modifies it (“cinema”).
So alamat bioskop = “the cinema’s address.”
Reversing them would break that pattern.

Why use di buku kecil instead of dalam buku kecil?

Di by itself already conveys “in” or “on” in many contexts.
Di dalam (“inside”) is more formal or emphatic but not required here.
Everyday speech drops dalam and simply says di buku kecil = “in a small notebook.”

What exactly is a buku kecil? Can I call it a “notebook”?

Buku kecil literally means “small book” and in context is understood as a little notebook or pocket diary.
You could also say buku catatan kecil (“small note-taking book”).
Although English speakers sometimes use notebook, native learners often say buku or buku catatan.

What does agar tidak lupa mean, and could I use supaya instead of agar?

Agar means “so that” or “in order to.”
Tidak lupa is “not forget,” so agar tidak lupa = “so that (I) won’t forget.”
Supaya works the same way and is interchangeable:
“Saya mencatat... supaya tidak lupa.”

Why is it tidak lupa instead of jangan lupa?

Tidak lupa is part of a subordinate clause expressing purpose: “so that I do not forget.”
Jangan lupa is an imperative meaning “don’t forget!” (a command to someone).
Here we need a neutral “not forget,” not a command.

Can I move di buku kecil to the front, like Di buku kecil saya mencatat alamat bioskop?

Yes, you can front the prepositional phrase for emphasis or style:
“Di buku kecil, saya mencatat alamat bioskop agar tidak lupa.”
But the original SVO order (Saya mencatat... di buku kecil...) is more neutral and common.

Do I need to repeat the subject before tidak lupa, like agar saya tidak lupa?

No, Indonesian allows dropping repeated subjects in subordinate clauses.

…agar tidak lupa is fine because it’s clear the subject (I) is the same.
If you want to be extra clear, you could say agar saya tidak lupa, but it’s not necessary.

Why is there no plural or possessive marker on bioskop? How do I know whose address it is?

Possessive relationships in noun compounds (e.g. alamat bioskop) don’t need markers.

Alamat bioskop already implies “the address of [a] cinema.”
If you wanted to specify “my” cinema, you’d need context or say bioskop saya (but that sounds like “my cinema,” which is odd here).

Could I shorten the sentence and still keep the meaning?

Yes. In casual speech you might say:
“Saya catat alamat bioskop di buku biar nggak lupa.”

catat (short for mencatat)
biar (colloquial for agar/supaya)
nggak (colloquial for tidak)