Learn Hardcore Turkish: Dolaptaki elbiseleri katladım, hepsini askıya astım. - I folded the clothes in the wardrobe and hung them all on hangers.

dolapta = “in the closet/wardrobe” (locative; an adverbial phrase of place)
dolaptaki = “the one(s) that are in the closet” (locative + -ki; turns it into an adjective)

Form: dolap + ta + ki → dolaptaki. The -ki suffix makes a relative-like adjective: “the X that is/are in/on/at Y.”

Examples:

Dolapta elbise katladım. = I folded clothes in the closet. (where the action happened)
Dolaptaki elbiseleri katladım. = I folded the clothes that are in the closet. (which clothes I folded)

Note the consonant in dolaptaki is t, not d, because the locative on a voiceless consonant is -ta/-te: dolapta → dolaptaki (not “dolapdaki”).

Why is elbiseleri in the accusative (-i)?

In Turkish, a definite/specific direct object takes the accusative. Dolaptaki elbiseleri is “the clothes (in the closet)”—a specific set—so you need -i:

Dolaptaki elbiseleri katladım. = I folded the clothes (in the closet). [definite] If you mean it indefinitely, you’d avoid -i and usually drop -ki as well:
Dolapta elbise katladım. = I folded (some) clothes in the closet. [indefinite]

Could elbiseleri mean “his/her/their clothes”? How do I say that if I want it?

Alone, elbiseleri can be ambiguous in other contexts (it can be “their clothes” as a possessed noun in the nominative), but in your sentence it functions as the definite plural object (“the clothes”). To clearly express possession with a direct object, add both the possessive and the accusative:

Onun elbiseleri burada. = His/Her clothes are here. (subject; nominative)
Onun elbiselerini katladım. = I folded his/her clothes. (object; accusative)
Onun dolaptaki elbiselerini katladım. = I folded his/her clothes that are in the closet.

Why is it hepsini and not hepsi?

Hepsi is nominative (“all [of them]” as a subject or predicate). As a definite object, it takes accusative: hepsini.

Hepsi askıda. = They’re all on the hanger(s). (predicate)
Hepsini askıya astım. = I hung them all (up). (object)

Does hepsini refer to elbiseleri? Could I say onları instead?

Yes, hepsini refers back to the clothes you just mentioned. You can say onları (“them”) but it doesn’t emphasize “all”:

Onları askıya astım. = I hung them. (neutral)
Hepsini askıya astım. = I hung all of them. (no exceptions)
For extra emphasis you can say Onların hepsini askıya astım.

What’s the “y” in askıya?

A buffer consonant. The dative is -a/-e, and when a word ends in a vowel, Turkish inserts y:

askı + a → askıya
kapı + a → kapıya
bina + e → binaya

Shouldn’t it be plural (askılara) since there are multiple clothes?

Both are fine; it depends on what you want to highlight.

Hepsini askıya astım. = I hung them on a hanger/on hangers (generic destination; natural and common).
Hepsini askılara astım. = I hung them onto (multiple) hangers (emphasizes the plurality of hangers).

Which case does asmak take? Can I use -da?

For the target you hang something onto, asmak takes the dative (-a/-e):

… askıya asmak = to hang on(to) a hanger Use the locative (-da/-de) to describe the resulting location/state:
Hepsi askıda. = They’re all on the hanger(s).
Hepsini askıya astım. = I hung them on the hanger(s).

How are the past forms katladım and astım built?

katla- (stem) + -dı (past) + -m (1sg) → vowel harmony: katladım
as- (stem) + -dı (past) + -m (1sg) → after a voiceless consonant, the past becomes -tı; vowel harmony with “a” → astım

Can I connect the two actions in other ways than a comma?

Yes:

Dolaptaki elbiseleri katladım ve hepsini askıya astım. (with “ve” = and)
Dolaptaki elbiseleri katlayıp hepsini askıya astım. (-ıp links sequential same-subject actions smoothly) All are natural.

Can I say Dolapta instead of Dolaptaki?

Different meaning:

Dolapta elbiseleri katladım. = I folded the clothes in the closet (location of the action).
Dolaptaki elbiseleri katladım. = I folded the clothes that are in the closet (identifies which clothes). Use -taki/-deki when you want “the one(s) that are in/on/at …,” not just the place of the action.

Is using elbise for “clothes” natural, or should I use kıyafet/giysi?

elbise often means “dress” (a specific garment), though some speakers do use it broadly for clothes.
For general “clothes,” kıyafet (very common) or giysi (more formal/neutral) are safer. Examples:
Dolaptaki kıyafetleri katladım.
Dolaptaki giysileri katladım.

Can I omit hepsini?

Yes. Dolaptaki elbiseleri katladım, askıya astım. still works. Hepsini simply adds “all (of them),” emphasizing completeness.

Where does hepsini usually go in the sentence?

Before the verb, and typically before other complements:

Most natural: Hepsini askıya astım.
Acceptable but marked for emphasis: Askıya hepsini astım. (puts focus on “askıya”) Object pronouns like hepsini usually sit right before the verb.