Sorunun farkındayım.

The base noun is sorun = problem / issue.

Here it appears as sorun + -un, where -un is the genitive ending, so sorunun means of the problem.

The ending is -un because of vowel harmony. Turkish genitive has four common forms:

• -ın
• -in
• -un
• -ün

Since sorun has the vowel u in its last syllable, -un is the correct form.

Because farkında olmak uses a genitive noun before it.

So Turkish says:

• X-in farkında olmak = to be aware of X

That is why you get:

• sorunun farkındayım = I am aware of the problem

If you used sorunu, that would be the accusative form, which is used for direct objects, and it does not fit this pattern.

farkındayım can be broken down as:

• farkında = aware
• -yım = I am

So farkındayım means I am aware.

The -y- is just a buffer consonant. It appears because the ending is attached to a word that already ends in a vowel.

So:

• farkında + yım → farkındayım

In Turkish, the present-tense form of to be is often shown with a personal ending, not a separate word.

So instead of saying something like I am aware with a separate verb, Turkish attaches the I am meaning directly to the predicate:

• farkındayım = I am aware
• farkındasın = you are aware
• farkında = he/she/it is aware

This is very normal Turkish grammar.

In everyday Turkish, you should learn farkında olmak as a set expression meaning to be aware / to realize / to be conscious of.

Historically, farkında comes from fark and older grammatical pieces, but for learners the important thing is this pattern:

• bir şeyin farkında olmak = to be aware of something

Examples:

• Durumun farkındayım. = I am aware of the situation.
• Hatanın farkında değilim. = I am not aware of the mistake.

So yes, it behaves a bit like an adjective in the sentence, but it is best learned as part of the full expression.

Yes, by itself sorunun can be ambiguous.

It can mean:

• of the problem — genitive form of sorun
• your problem — 2nd person singular possessive form

But in Sorunun farkındayım, the grammar strongly points to of the problem, because farkında olmak expects the genitive.

If you wanted to say I am aware of your problem, Turkish would usually be:

• Sorununun farkındayım.

That looks longer because your problem already has a possessive ending, and then the whole phrase also gets the genitive needed by farkında olmak.

Yes, absolutely.

Ben is optional because -yım already tells you the subject is I.

So:

• Sorunun farkındayım.
• Ben sorunun farkındayım.

Both are correct.

Using ben can add emphasis, contrast, or clarity. For example:

• Ben sorunun farkındayım, ama o değil.
  I am aware of the problem, but he isn't.

For the negative, Turkish usually uses değil with this structure:

• Sorunun farkında değilim. = I am not aware of the problem.

For the past:

• Sorunun farkındaydım. = I was aware of the problem.

For a question:

• Sorunun farkında mısın? = Are you aware of the problem?

So once you know X-in farkında olmak, you can build many useful sentences with it.