Learn Hardcore Indonesian: Ketika pelangi muncul, anak-anak tersenyum; mereka pasti bahagia. - When the rainbow appears, the children smile; they are surely happy.

saat: very common and neutral. Example: Saat pelangi muncul, ...
waktu: more colloquial when used as a conjunction. Example: Waktu pelangi muncul, ... Very formal/literary options: tatkala, sewaktu. For immediacy, use begitu (as soon as): Begitu pelangi muncul, ...

Why is there a comma after Ketika pelangi muncul?

In Indonesian, when a subordinate clause comes first, you put a comma after it. If you reverse the order, you typically drop the comma:

Ketika pelangi muncul, anak-anak tersenyum.
Anak-anak tersenyum ketika pelangi muncul.

Why is there a semicolon before mereka pasti bahagia? Could I use a comma or a period instead?

The semicolon separates two independent but closely related clauses without a conjunction.
A period is also fine: ... anak-anak tersenyum. Mereka pasti bahagia.
If you want a comma, add a conjunction: ..., jadi/maka mereka pasti bahagia.
In formal writing (PUEBI), a plain comma between two independent clauses (comma splice) is discouraged.

Is anak-anak the only way to say “children”? What’s the role of the hyphen?

Anak means child, but can also be generic/plural from context.
Anak-anak is reduplication (marked with a hyphen) to emphasize plurality: children.
You can also use para with human nouns to mark plural groups, but it’s more formal and not used with reduplication. Prefer anak-anak. You may see para anak in certain phrases (often followed by a descriptor: para anak jalanan), but para anak-anak is incorrect.

Why tersenyum? What about senyum or bersenyum?

Tersenyum is the standard intransitive verb “to smile,” very common.
Bersenyum is also correct and means the same; stylistic preference varies.
Senyum as a verb (without prefix) is colloquial: Dia senyum.
Tersenyum-senyum suggests repeated/lingering smiling (often to oneself).
To indicate a recipient, add a preposition: tersenyum/bersenyum kepada/ke seseorang.

Why is there no “to be” before bahagia? Why not mereka adalah bahagia?

Indonesian adjectives can function as predicates without a copula. So mereka bahagia is correct and natural. Adalah is used primarily before noun phrases, not before adjectives.

Does pasti mean “must” as in obligation?

No. Pasti expresses certainty/inference (“surely, certainly”), like English “must be” in the evidential sense. Obligation “must/ have to” is harus. So:

Mereka pasti bahagia = They must be (surely are) happy.
Mereka harus bahagia = They must be happy (they are required/obliged to be happy).

Where can pasti go, and what are alternatives like tentu or pastinya?

Neutral: Mereka pasti bahagia.
Emphatic fronting: Pasti mereka bahagia.
Tag-like/informal: Mereka bahagia, pasti.
Emphatic particle: Mereka pastilah bahagia. Alternatives:
Tentu / tentu saja = certainly (often sounds a bit more polite/expected).
Pastinya = for-sure; colloquial stance marker.
To hedge instead of assert: sepertinya (it seems).

Could I also say Ketika muncul pelangi instead of Ketika pelangi muncul?

Yes, both orders are grammatical. Ketika pelangi muncul is the more neutral order. Ketika muncul pelangi is also acceptable and can sound slightly more narrative/dynamic (“when there appeared a rainbow”). You can add itu for specificity: Ketika pelangi itu muncul, ...

Is muncul the best verb for a rainbow? How does it differ from terlihat/nampak?

Muncul = “to appear/show up” (event of appearing). Natural with pelangi.
Terlihat/nampak = “to be visible/seen” (state of being visible). Slightly different nuance: Ketika pelangi terlihat, ...
For noun forms: kemunculan (appearance). Example: Dengan kemunculan pelangi, anak-anak tersenyum.

Can I drop mereka in the second clause to avoid repetition?

You can in informal style: Ketika pelangi muncul, anak-anak tersenyum; pasti bahagia. It will be understood from context. In careful or formal writing, keeping mereka avoids ambiguity and reads better.

What’s the difference between bahagia, senang, and gembira here?

Bahagia: deep/lasting happiness or contentment (life-level happiness).
Senang: pleased/glad/content (lighter, situational).
Gembira: joyful/cheerful (often lively, celebratory). You could say mereka senang/gembira, but bahagia suggests a stronger or deeper happiness.

How do I make the timing clearer (past, ongoing, habitual, future)?

Indonesian has no tense marking; use time/aspect words:

Past: Ketika pelangi muncul tadi/kemarin, ...
Ongoing: Ketika pelangi sedang muncul, ... (rare for rainbows; more natural: baru saja)
Habitual: Setiap kali pelangi muncul, anak-anak tersenyum.
Future: Kalau nanti pelangi muncul, anak-anak akan tersenyum.

Could I add pun after anak-anak? What does it do?

Yes: Ketika pelangi muncul, anak-anak pun tersenyum; ... The particle pun adds a mild “even/too/also/then” flavor, marking a natural consequence or inclusion. It’s stylistic and common in narrative writing.