Ben haksız olduğumu anlayınca hemen özür diliyorum.

Yes. Turkish often drops subject pronouns because the verb already shows the person.

Here, diliyorum already means I am apologizing / I apologize, so Ben is not strictly necessary. The sentence could simply be:

Haksız olduğumu anlayınca hemen özür diliyorum.

Adding Ben can give a little extra emphasis or clarity, especially if the speaker wants to stress I.

As a whole, haksız olduğumu means that I am wrong or that I’m in the wrong.

It is made of:

• haksız = wrong, unjust, at fault
• olduğumu = that I am / that I was

So literally, it is something like:

my being wrong
or
that I am wrong

In this sentence, it is the thing being realized.

Olduğumu can be broken down like this:

• ol- = to be / become
• -duk / -dık / -dik / -dük = a suffix used to make a subordinate clause like that ...
• -um = my, marking that the subject of that clause is I
• -u = accusative case, because this whole clause is the object of anlamak

Because of sound changes, ol + duk + um + u becomes olduğumu.

So olduğumu literally means something like that I am or that I was, depending on context.

The final -u is the accusative marker.

That is there because anlamak usually takes an object: you understand or realize something. In this sentence, the something is the whole clause:

haksız olduğumu = that I am wrong

So Turkish marks that clause as the direct object of anlayınca.

Because Turkish is not using a full main clause here. It is using a subordinate clause that functions like that I am wrong.

• haksızım = I am wrong as a complete sentence
• haksız olduğumu = that I am wrong as part of a bigger sentence

English does something similar:

• I am wrong.
• I realize that I am wrong.

So in Turkish, when a clause is embedded inside another sentence, it often gets turned into this noun-like structure with endings such as -DIK and a possessive ending.

Not necessarily.

This is a very common confusion. In olduğumu, the -duğ- part comes from the -DIK subordinate-clause pattern. It does not behave exactly like a simple past tense verb in English.

So haksız olduğumu can often mean:

• that I am wrong
• that I was wrong

The exact time reference depends on the context.

In this sentence, the natural meaning is usually that I am wrong / that I’m in the wrong.

Anlayınca means when (I) realize or upon realizing.

It comes from:

• anla- = understand, realize
• -yınca = when / once / upon

Because the verb stem ends in a vowel, Turkish adds a buffer y:

anla + yınca = anlayınca

So the idea is:

when I realize that I am wrong...

Because Turkish often uses suffixes instead of separate linking words.

In English, you say:

when I realize

In Turkish, you can attach a suffix directly to the verb:

anlayınca

This is very natural Turkish. The suffix -ınca / -ince / -unca / -ünce often means:

• when
• once
• as soon as
• upon

depending on context.

The subject of anlayınca is understood from context, and here it is the same as the subject of the main verb: I.

So the sentence means:

When I realize that I am wrong, I apologize immediately.

In Turkish, these -ınca clauses often share their subject with the main clause unless something else makes the subject clear.

Since the sentence already has Ben and the main verb is diliyorum, the subject is clearly I throughout.

Yes, dilemek on its own often means to wish or to request, but özür dilemek is a fixed expression meaning:

to apologize

Literally, it is closer to to ask for forgiveness / to express apology, but in normal English the best translation is simply to apologize.

So:

• özür = apology
• dilemek = to ask/request/wish
• özür dilemek = to apologize

This is a standard verb phrase in Turkish.

Because Turkish uses the expression özür dilemek, not a simple verb made directly from özür.

So you say:

• özür diliyorum = I apologize
• özür diledim = I apologized
• özür dileyeceğim = I will apologize

You do not normally say özürlüyorum for I apologize.

Diliyorum here can express a habitual or general action, especially in a sentence like this:

When I realize that I am wrong, I apologize immediately.

In Turkish, the -yor form is often used not only for actions happening right now, but also for regular behavior, especially in everyday speech.

So hemen özür diliyorum can mean:

• I apologize immediately
• I’m quick to apologize
• I do apologize right away

An aorist form such as dilerim is possible in some contexts, but diliyorum sounds very natural and common here.

Because Turkish adverbs often come before the verb or verb phrase they modify.

So:

• hemen = immediately
• özür diliyorum = I apologize

Putting them together as hemen özür diliyorum means I apologize immediately.

This is a very normal word order in Turkish.

Yes, to some extent. Turkish word order is more flexible than English, but the given version is very natural.

The sentence:

Ben haksız olduğumu anlayınca hemen özür diliyorum.

has a very typical flow:

1. subject
2. object/subordinate clause
3. time-related clause
4. adverb
5. main verb

You could omit Ben, and some other rearrangements are possible, but the original sentence sounds smooth and standard. The most important thing is that the verb usually comes near the end, and the clause haksız olduğumu naturally appears before anlayınca, since it is what is being realized.