Learn Hardcore Indonesian: Dia meletakkan kaus kaki di dekat jendela agar cepat kering. - He/She puts the socks near the window so that they dry quickly.

Meletakkan = to put/place something down somewhere (often slightly more formal or careful-sounding).
Menaruh = to put/place (very common in everyday speech).
Taruh = the root; used in imperatives/informal speech (Taruh di sini! Put it here!). All three can work here. Your sentence with menaruh would sound a bit more casual: Dia menaruh kaus kaki…

Why does the verb have the suffix -kan? Could I say "meletak"?

No. The root is letak (“position”). The verb is formed as meN- + letak + -kan → meletakkan, meaning “to place [something] (somewhere).”

The suffix -kan often makes the verb causative/applicative (cause something to be in a position).
There’s no standard verb meletak.
Spelling: it’s meletakkan with double k (from the -kan suffix), not “meletakan.”

Does "dia" mean “he” or “she”? How can I be specific?

Dia can mean either “he” or “she”; Indonesian doesn’t mark gender. To clarify, add a noun: dia laki-laki (he), dia perempuan (she), or simply use the person’s name. For respectful reference, use beliau (usually in the 3rd person).

How do I say “his socks,” “her socks,” or “the socks”?

“His/her socks” = kaus kakinya (the suffix -nya marks possession or definiteness).
“The socks” (specific) = kaus kaki itu. Without markers, kaus kaki can be “sock/socks” in a general sense.

Is "kaus kaki" singular or plural? How do I say “a pair of socks” or “two pairs”?

Indonesian usually doesn’t mark plural. Context tells you.

A pair of socks = sepasang kaus kaki.
Two pairs of socks = dua pasang kaus kaki.
One sock = satu kaus kaki.

Which spelling is correct: "kaus kaki" or "kaos kaki"?

Both are widely understood. Kaus kaki is the recommended standard spelling; kaos kaki is very common in everyday writing and speech.

Why is it "di dekat jendela" and not "ke dekat jendela" or just "dekat jendela"?

di marks location (“at/in/on”), so di dekat jendela = “near the window.”
ke marks movement toward a place, so ke dekat is not used.
You might hear dekat jendela without di, but di dekat jendela is the safest, most neutral phrasing.

What’s the nuance difference between "di dekat," "di samping," and something like "di ambang jendela"?

di dekat jendela = near the window (not necessarily touching).
di samping jendela = next to the window (beside it).
di ambang jendela = on the windowsill/at the window ledge (on the threshold).

What does "agar" do here? Can I use "supaya," "biar," or "untuk" instead?

Agar introduces a purpose clause: “so that/in order that.” Alternatives:

supaya: very common and neutral (Dia … supaya cepat kering).
biar: more informal/colloquial.
untuk usually takes a noun or verb phrase, not an adjective: not natural to say “untuk cepat kering.” You could say untuk mempercepat pengeringannya (very formal).

Why is it "agar cepat kering" and not "dengan cepat" or "menjadi kering"?

cepat can function adverbially: cepat kering = “dry quickly.” Very idiomatic.
dengan cepat is also correct but slightly heavier here.
menjadi kering (“become dry”) is grammatical, but agar cepat kering sounds more natural and concise in speech.

Could I say "agar cepat mengering" instead of "agar cepat kering"?

Yes. cepat mengering focuses on the process (“dry quickly”), while cepat kering focuses on reaching the dry state quickly. Both are common and acceptable.

How would this look in the passive voice?

Kaus kaki diletakkan di dekat jendela agar cepat kering. You can add the agent if needed: Kaus kaki diletakkan di dekat jendela oleh dia, but Indonesians usually omit oleh dia if it’s clear.

How do I show past or future time, since there’s no tense marking?

Add time words or auxiliaries:

Past/completed: tadi, kemarin, sudah/telah (Dia sudah meletakkan…).
Future/intended: nanti, besok, akan (Dia akan meletakkan…).

Can I move the purpose clause to the front?

Yes: Agar cepat kering, dia meletakkan kaus kaki di dekat jendela. This is natural and common for emphasis on purpose.

Is there a more “drying-specific” verb than "meletakkan"?

Yes:

menjemur = put out to dry (usually in the sun/air). Works if sunlight/airflow by the window is intended: Dia menjemur kaus kaki di dekat jendela…
mengeringkan = to dry something (actively, e.g., with a dryer/hairdryer).
mengangin-anginkan = air out (let air dry).

Any tip about "di" as a preposition vs the passive prefix "di-"?

di (preposition) is separate: di dekat, di meja.
di- (passive prefix) attaches to the verb: diletakkan. Don’t write “didekat jendela”; it must be di dekat jendela.