Dayım kayısıları yıkadıktan sonra onları buzdolabına koydu.

Dayım means my maternal uncle — specifically, your mother’s brother.

Breakdown:

• dayı = maternal uncle
• -ım = my

So:

• dayım = my uncle (mother’s brother)

Turkish often distinguishes family relations more specifically than English:

• dayı = mother’s brother
• amca = father’s brother

Kayısıları is the definite direct object form.

Breakdown:

• kayısı = apricot
• kayısılar = apricots
• kayısıları = the apricots / those apricots as a specific object

In Turkish, a specific/definite direct object usually takes the accusative suffix.

So here:

• kayısıları yıkadı = he washed the apricots
• kayısılar yıkadı would be incorrect here
• kayısı yıkadı would mean he washed an apricot or apricot in a very different structure

Yes, in some contexts it can.

That is because -ları can sometimes be interpreted as:

• plural marker + accusative, or
• possessive-related structure in other contexts

But in this sentence, the natural reading is:

• kayısıları = the apricots as the object of washed

Why?

• The sentence structure strongly supports that meaning.
• The following onları also refers back to those apricots.

So although kayısıları can be ambiguous in isolation, here it is best understood as the apricots.

Yıkadıktan sonra means after washing or more literally after he washed.

It is built with the common Turkish pattern:

verb + -DIktan sonra = after doing ...

So here:

• yıka- = wash
• yıkadıktan sonra = after washing / after he washed

Examples:

• geldikten sonra = after coming / after he came
• yemek yedikten sonra = after eating

This structure is very common in Turkish for linking actions in time.

By default, it is understood to be the same subject as in the main clause.

So in this sentence:

• Dayım ... yıkadıktan sonra ... koydu
• both actions are understood as being done by my uncle

So the meaning is:

• After my uncle washed the apricots, he put them in the refrigerator.

If the subject were different, Turkish would normally make that clear from context or by stating it explicitly.

Yes, but they belong to different verbs.

Structure:

• kayısıları yıkadıktan sonra = after washing the apricots
• onları buzdolabına koydu = he put them into the refrigerator

So:

• kayısıları is the object of washing
• onları is the object of putting

English works the same way:

• After washing the apricots, he put them in the refrigerator.

You mention the noun first, then later use a pronoun to refer back to it.

Yes, it often can.

Turkish frequently drops pronouns when the meaning is already clear.

So this would also be natural:

• Dayım kayısıları yıkadıktan sonra buzdolabına koydu.

That still means:

• After washing the apricots, my uncle put them in the refrigerator.

Including onları makes the reference a little more explicit, and can sound slightly more natural depending on style and context.

Onları is the accusative form of onlar.

Breakdown:

• onlar = they / them
• onları = them (as a specific direct object)

Since koymak takes a direct object here, and the object is specific, Turkish uses the accusative form:

• onları koydu = he put them

Because the sentence describes movement toward a place, not simple location.

• buzdolabına = to / into the refrigerator
• buzdolabında = in / inside the refrigerator

With koymak (to put/place), Turkish normally uses the dative:

• masaya koydu = put it on the table
• çantaya koydu = put it into the bag
• buzdolabına koydu = put it into the refrigerator

If you said buzdolabında, that would describe where something is, not where it is being placed.

That -n- is a buffer consonant.

The word buzdolabı ends in a vowel sound, and when certain suffixes are added, Turkish often inserts -n- to make pronunciation smoother.

So:

• buzdolabı = refrigerator
• buzdolabına = to/into the refrigerator

This happens especially after forms that contain a third-person possessive-type ending, which many compound nouns like buzdolabı have historically/formally in their structure.

For a learner, the most practical thing is simply to remember:

• buzdolabı
• buzdolabına
• buzdolabında
• buzdolabından

Koydu means he/she put.

Breakdown:

• koy- = put, place
• -du = past tense

So:

• koydu = he/she put

Turkish usually does not need a separate word for he or she, because the verb form and context are enough.

Because Turkish is typically a verb-final language.

A neutral Turkish sentence often puts the main verb last:

• Dayım ... koydu.

Also, subordinate time expressions like yıkadıktan sonra commonly come before the main verb.

So the overall order feels natural in Turkish:

• Dayım kayısıları yıkadıktan sonra onları buzdolabına koydu.

A very literal structural gloss would be:

• My uncle, after washing the apricots, put them into the refrigerator.

That verb-final pattern is one of the biggest differences from English.

Yes, Turkish word order is flexible, but not completely free.

This sentence uses a very natural, neutral order:

• Dayım kayısıları yıkadıktan sonra onları buzdolabına koydu.

You can move some parts for emphasis, but the verb usually still stays near the end:

• Dayım onları, kayısıları yıkadıktan sonra, buzdolabına koydu.

That sounds more marked and emphasizes onları.

So:

• this sentence’s order = natural and standard
• other orders = possible, but usually used for emphasis, contrast, or style