Çamaşırlar kurudu mu onları katlayıp dolaba koyacağım.

Because Turkish often uses a singular verb with an inanimate plural subject. Çamaşırlar kurudu is the normal, natural way to say that the clothes dried / are dry.

Using kurudular would sound marked or stylistic here, not the default everyday form.

Here kurudu mu does not function as a normal yes/no question like Did it dry?
In this structure, verb + -DI + mı/mi/mu/mü often means:

• when
• once
• as soon as
• sometimes if

So Çamaşırlar kurudu mu... means something like When/Once the clothes are dry...

Because the Turkish question particle mı/mi/mu/mü is written as a separate word. That is true even when it is used in patterns like this one.

So you write:

• kurudu mu
• geldi mi
• hazır mı

not as one combined word.

The form changes by vowel harmony. The question particle has four forms:

• mı
• mi
• mu
• mü

It matches the last vowel of the word before it. Since kurudu ends with the vowel u, the correct form is mu.

It could be omitted if the meaning is clear from context. Turkish often leaves out objects that are already understood.

So Çamaşırlar kurudu mu katlayıp dolaba koyacağım is also possible.

But onları makes the object explicit: them. It helps clearly connect the two actions katlayıp and koyacağım to the clothes.

Onları is the accusative form of onlar. Here it means them as a definite, specific object.

Breakdown:

• onlar = they / them
• onları = them, as a definite direct object

Since the speaker is talking about specific clothes already mentioned, the accusative form is natural.

Katlayıp comes from katlamak and uses the converb suffix -(y)ıp / -(y)ip / -(y)up / -(y)üp.

It links actions and often means:

• and ...
• after ...-ing
• ... then ...

So katlayıp dolaba koyacağım means I’ll fold them and put them in the closet or after folding them, I’ll put them in the closet.

The y appears because katla- ends in a vowel.

Because dolaba is the dative form of dolap and shows movement to / into something.

• dolap = closet, cabinet, cupboard
• dolaba = to the closet / into the closet

This fits koymak, because you put something into a place.

Also notice the consonant change:

• dolap → dolaba

That is a normal consonant softening pattern in Turkish.

It breaks down like this:

• koy- = put
• -acak / -ecek = future
• -ım / -im / -um / -üm = I

So koyacağım means I will put.

You may notice the k of the future suffix becomes ğ before the personal ending:

• koyacak
• koyacağım

Because Turkish often drops subject pronouns when the verb already shows the person.

In koyacağım, the ending already tells you the subject is I. So ben is not necessary.

You could say Ben koyacağım, but that would add emphasis, contrast, or special focus.

Not completely, but this order is very natural. Turkish commonly puts the time/condition clause first and the main verb near the end.

So this pattern is very typical:

• Çamaşırlar kurudu mu = when the clothes are dry
• onları katlayıp dolaba koyacağım = I’ll fold them and put them in the closet

Some parts can move for emphasis, but the given order is smooth and neutral.

Yes, but the nuance changes a little.

• kuruyunca = when/once they dry
• kurursa = if they dry
• kurudu mu = once/when they are dry, often with a conversational feel

So all three can work in similar situations, but kurudu mu is a very common way to express once that happens, then...