Learn Hardcore Indonesian: Saya memesan lauk ayam di kantin sekolah. - I order a chicken side dish at the school canteen.

memesan = to order (food/drinks) or to book/reserve. It’s slightly more formal/neutral.
pesan (without the prefix) is very common in everyday speech: Saya pesan lauk ayam…
membeli = to buy. It focuses on the purchase, not the act of telling someone what you want. At a canteen both are possible, but:
- memesan suggests placing an order.
- membeli suggests buying a ready-made item. Examples:
Saya memesan lauk ayam. I ordered a chicken dish.
Saya pesan lauk ayam. (colloquial) I order/ordered a chicken dish.
Saya membeli lauk ayam. I bought a chicken dish.

What exactly does lauk mean? Is lauk ayam natural?

lauk = “side dish” eaten with rice; the protein/vegetable dishes that accompany rice.
lauk ayam = a chicken side dish. It’s natural, especially in canteen/warteg contexts where people talk about types of lauk (e.g., lauk ayam, lauk ikan, lauk tempe).
In casual ordering, many people just name the item (e.g., ayam goreng, “fried chicken”).

How do I say “a portion/piece of chicken” in this context?

Use classifiers/measure words:

How do I distinguish “a chicken dish” vs “the chicken dish” in Indonesian?

Indonesian has no articles (a/the). You indicate definiteness with:

itu after the noun: lauk ayam itu = that/the chicken dish
-nya attached: lauk ayamnya = the chicken dish (context-known)
Indefinite “a” is often just the bare noun, or you use a classifier: seporsi lauk ayam. Examples:
Saya memesan lauk ayam itu. I ordered the chicken dish (we both know which one).
Saya pesan lauk ayamnya satu. I’ll have one portion of the chicken dish.

Why is it di kantin sekolah and not ke kantin sekolah?

di = at/in (location).
ke = to (movement/destination). Your sentence states where the ordering happened (location): di kantin sekolah. If you talk about going there: Saya pergi ke kantin sekolah untuk memesan lauk ayam.

Can I say kantin di sekolah instead of kantin sekolah? Any difference?

Both are acceptable but with a slight nuance:

kantin sekolah = the school’s canteen (possessive/affiliation).
kantin di sekolah = a canteen located at a school (more purely locative). In your sentence, di kantin sekolah is smooth and idiomatic.

Why is it kantin sekolah and not sekolah kantin? How does noun–noun modification work?

Indonesian puts the head noun first and the modifier second:

kantin sekolah = school canteen
Reversing to sekolah kantin is ungrammatical. More examples:
tas sekolah (school bag), teman sekolah (school friend), meja kantor (office desk).

Is di here the passive prefix? How do I tell di (preposition) from di- (passive prefix)?

Preposition di (at/in) is written separately: di kantin.
Passive prefix di- attaches to a verb: dipesan (is/was ordered). Example:
Active: Saya memesan lauk ayam di kantin sekolah.
Passive: Lauk ayam dipesan (oleh saya) di kantin sekolah.

How do I show past, present, or future? Does this sentence mean past?

Indonesian doesn’t mark tense on the verb. Use time/aspect words:

Can I start with the place: “At the school canteen, I ordered…”?

Yes. Di kantin sekolah, saya memesan lauk ayam. Placing the location first is natural for emphasis or topic-setting.

Is Saya the best pronoun here? What about Aku or gue?

Saya: neutral/polite; safe in most situations.
Aku: informal/intimate with friends/family.
gue/gua: very informal Jakarta slang. All fit grammatically: Aku/Saya/gue memesan/pesan lauk ayam… Choose based on formality and audience.

Is it okay to say Saya pesan instead of Saya memesan?

Yes. In conversation, dropping the prefix is very common:

Saya pesan lauk ayam di kantin sekolah. (colloquial) It sounds a bit more casual than Saya memesan….

How would people naturally order this at a counter?

Common patterns:

Mbak/Mas, ayam gorengnya satu, ya.
Saya mau ayamnya satu.
Ayamnya masih ada? Saya pesan satu. Notes: -nya makes it “the one we’re talking about,” mau softens the request, ya is a polite softener.

How do I say “my school canteen”?

Use a possessive:

kantin sekolah saya (neutral)
kantin sekolahku (more informal) Example: Saya memesan lauk ayam di kantin sekolah saya.

Does memesan also mean “to reserve/book”? What about the related nouns?

Yes: memesan kamar hotel, memesan meja, memesan tiket.
pesanan = the order (thing ordered): Pesanan saya sudah siap?
pemesanan = the act/system of ordering/reservation: Pemesanan dilakukan secara online.