Dayım erik almış olmalı, çünkü mutfakta erik dolu bir torba gördüm.

Dayım means my maternal uncle.

In Turkish, family words can be more specific than in English:

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

The ending -ım means my. So:

• dayı = maternal uncle
• dayım = my maternal uncle

The vowel in the suffix changes because of vowel harmony, so here it becomes -ım.

Turkish often uses the bare singular noun where English would use a plural like plums.

So erik almak can mean:

• to buy plums
• to buy some plums

It does not have to mean just one plum.

The word erik appears twice because it has two different jobs:

• Dayım erik almış olmalı = the thing bought was plums
• erik dolu bir torba = the bag was full of plums

Using erikler would put more emphasis on a definite plural set, which is not necessary here.

This is about the Turkish accusative.

In Turkish, a direct object is often left unmarked when it is indefinite or non-specific.

• erik aldı = he bought plums / some plums
• eriği aldı = he bought the plum / the specific plum

So in this sentence, erik means the speaker is not referring to a particular previously known plum or set of plums. It is just some plums in a general sense.

Almış olmalı is a very common way to say must have bought.

It is made of:

• al- = buy
• -mış = a form that often points to a completed action, often with an inferred or non-direct nuance
• olmalı = must be / should be

Together, almış olmalı expresses a deduction about the past:

• Dayım erik almış olmalı = My uncle must have bought plums

The speaker did not see the buying happen, but is concluding it from evidence.

No, they are very different.

• almalı = should buy / ought to buy
• almış olmalı = must have bought

So:

• Dayım erik almalı = My uncle should buy plums
• Dayım erik almış olmalı = My uncle must have bought plums

The first is about obligation.
The second is about deduction.

Because olmalı alone does not give the same time meaning.

Compare these:

• almalı = should buy
• alıyor olmalı = must be buying
• almış olmalı = must have bought

So the -mış part helps show that the action is understood as already completed. It is what makes the whole expression match English must have bought.

Because Turkish normally follows Subject-Object-Verb order, and the verb usually comes at the end of the clause.

First clause:

• Dayım = subject
• erik = object
• almış olmalı = verb phrase

Second clause:

• mutfakta = place
• erik dolu bir torba = object
• gördüm = verb

So the sentence structure is very normal Turkish. Word order can change for emphasis, but verb-final order is the default.

Literally, erik dolu bir torba means a bag full of plums.

• dolu = full
• erik dolu = full of plums
• bir torba = a bag

This pattern is very common in Turkish:

• kitap dolu oda = a room full of books
• insan dolu sokak = a street full of people
• su dolu bardak = a glass full of water

So noun + dolu works like full of + noun in English.

Because the locative suffix has two forms:

• -da / -de
• -ta / -te

The choice depends on the final consonant of the word. After a voiceless consonant, Turkish uses -ta / -te.

Mutfak ends in k, which is voiceless, so:

• mutfak + ta = mutfakta

This means in the kitchen.

Because the speaker is talking about something they personally saw.

• gördüm = I saw
• görmüşüm = apparently I saw / it turns out I saw

Since the evidence comes from direct personal observation, gördüm is the natural choice.

This creates a nice contrast in the sentence:

• the speaker directly saw the bag
• the speaker infers that the uncle bought the plums

In Turkish, a comma before çünkü is very common when it connects two full clauses.

So this is normal:

• Dayım erik almış olmalı, çünkü mutfakta erik dolu bir torba gördüm.

In English, punctuation with because is different, but in Turkish the comma here is natural and common.

Usually, çünkü introduces an explanation after the main statement, so this order is the most natural:

• Dayım erik almış olmalı, çünkü...

If you want to put the reason first, Turkish more naturally uses another structure, often -dığı için:

• Mutfakta erik dolu bir torba gördüğüm için dayım erik almış olmalı.

So yes, the idea can come first, but usually not with çünkü in the same way English uses because.

Yes, but the meaning changes.

• Dayım erik almış olmalı = My uncle must have bought plums
  Strong deduction

• Dayım erik almış olabilir = My uncle may/might have bought plums
  Weaker possibility

• Dayım erik almıştır = My uncle has probably bought plums / surely bought plums
  This can also sound inferential, but it is often more formal or stylistically different from almış olmalı

So almış olmalı is a very natural choice when the speaker is making a fairly strong guess from visible evidence.