My actual question is: what is the lexical category of the underlined word in the third sentence (sürece)? Adverb or sth else?

I would say it is a subordinating conjunction.

Daha önceki çalışmaları incelemedikleri sürece is adverb complement. You cant seperate them.

Hmm I checked what an adverb complement is here.

I think it´s adverbial clause.

-diğim/-diğin/diği/etc. sürece is listed as a "zarffiil" (approximate English term for it is gerundive) suffix which gives the meaning "as/so long as ...".

Yaşadığım sürece ... = As long as I live, ...

Ben yaşadıkça ... = As long as I live, ...

Ölmediğim sürece ... = So long as I don´t die, ...

Ben ölmedikçe ... = So long as I don´t die, ...

Yes that wholeness is an adverbial phrase in that sentence. But we can go further in specifying its constituents until single morpheme level. There is even an embedded sentence inside that phrase!

And the question was what is the function of sürece (as a part of that phrase of course). Or alternatively, why is sürece not like güzelce in sentence II?

I looked for a translation for "zarf tümleci" but I couldnt find a one. So I translated it that way. I hate grammar terms

"sürece" should always goes with "-diği". It doesn´t have any usage without it (at least I cannot think of any). If anyone can find anything otherwise let me know.

Addition:

Also we have "-ceği sürece" in parallel with "-diği sürece" but that should be it. If you google to find somthing you shouldn´t be confused with "sürec-e" (süreç=process sürece=to the process).

So correct question should ask about -diği sürece as a whole.

This was a question in the YGS exam which is the higher education examination in Turkey. In the exam I first thought that "sürece" was an adverb. But I certainly know that çocukça and genişçe are both adjectives so the answer is "I and V".

I just couldn´t figure out why "sürece" and "güzelce" are not the same. The answer is "I and V" so that means "sürece" cannot be an adverb according to the question. Can we say "-diği sürece" is an adverbial clause or "Daha önceki çalışmaları incelemedikleri sürece" is an adverbial clause as a whole? Can´t we talk about the function of "sürece" as a single word?

I and V is correct as you say. Because they are both adjectives. As you can see they describe a noun comes after them.

II is adverb becuse it describes the verb (dinlemek) not a noun.

III is part of a adverbal phrase.

IV is a noun.

sürece is a conjunction which is typically used for creating adverbial clauses. (If you translated that sentence into English there would also be a subordinating conjunction like until in the sentence - in the Turkish sentence DIK represents that subordination.)

If it was için everyone would say it is a conjunction.