http://www.youtube.com/watch?v=nJXlrI8proI

ah be lan 

the advancedness of this question was so intense it blew my mind

thinking of "sürece" as an adverb makes sense, but what doesn´t make sense is: "if sürece is an adverb, why the correct answer for this question is ´I and V´ but not ´II and III´ ?"

Also there is something more that I can´t figure out. We are taught that "-ce suffix" (eşitlik eki) is a "çekim eki" (inflectional suffix). We say that çocukça and genişçe are adjectives, but if -ce suffix is a "çekim eki", they can´t be adjectives, they must remain as nouns, right?

 Me too! Some of these threads are getting like a PhD in philology.

 Sadly, I went to school during a period when the fashion for teaching English was not only "no conjugating of sentences" but also a real dumbing down so that verbs were "doing words", adjectives "describing words" and that was about it. However, it hasn´t stopped me learning fluent Turkish. I find the best way is to understand how the word is being used in the sentence:

1. Çocukça = childish. Well all loved him/her, despite his/her childish actions.

2. Güzelce = well/nicely. Listen well to what I have to say, then after that you can start work.

3. Sürece = while/during/all the time/ as long as.

Lit: It seems impossible for them to prepare a good project while they do not study earlier exercises.

Free: It is impossible for them to prepare a good project without studying/ unless they study earlier exercises.

4. Japonca = Japanese. The difficulty of the alphabet is a factor that makes Japanese so hard to learn.

5. Genişçe = wide/fairly wide. S/he prepared a fairly wide report on the subject and brought it to us.

Sorry Abla, I don´t think you understand nothing, it is just I don´t know much grammatical terms in English and that makes me unable to participate in the conversation that much. 

You think sürece is a conjunction (correct me if I am wrong). If conjunction means "bağlaç", I think sürece is not a conjunction because conjunctions connect two different sentences or two elements which have the same function. But "İyi bir proje hazırlamaları imkansız görünüyor" is a sentence but "Daha önceki çalışmaları incelemedikleri" is not. 

"için" is just like "sürece". And "için" is not a conjunction as well. I checked TDK dictionary and it says "için" is an edat (look here). [by the way, honestly I don´t know exactly differences between edat and bağlaç. I can´t understand why "de/da" is considered as bağlaç but not edat.]

"-ce" being a derivational suffix is certainly more logical. But according to curriculum "-ce" is called as "eşitlik eki" and it is an iflectional suffix and I think there is something wrong with that  It is categorized under "İsim çekim ekleri" but they say it can change the function of a word.

I believe there is a confusion about -ce suffix.

Firstly there are more than one -ce suffixes in Turkish (with same form but different function/stress). It has been covered many times here.

You can find many such topics using search box but this one seems good to me:

http://www.turkishclass.com/forumTitle_44592

Edat=preposition/postposition

Bağlaç=conjuction

Edat examples:

Benim için = For me

Benim ile =  With me

Bağlaç examples:

Sen ve ben = You and I

Geldi de gidebildik = He (finally) came and/so we could leave

As you can see above "de" connects 2 sentences.

Conjunctions are of three kinds, coordinating, subordinating and correlative.

1. Coordinating conjunctions connect two pieces of language of equal syntactic importance.

Geldi ve gidebildik. (MAIN CLAUSE + MAIN CLAUSE)

My guess is this is just about what bağlaç means. 

2. Subordinating conjunctions connect two pieces of language. One of them governs the other one syntactically.

Hasta olduğu için eve gelecek. (SUBCLAUSE/ADVERBIAL + MAIN CLAUSE)

This is edat. The same word also has a postposition use when seen together with a noun phrase.

3. Correlative conjunctions work in pairs to join pieces of language of equal value.

Ne çalışır ne çalıştırır. (MAIN CLAUSE + MAIN CLAUSE)

Our original example is of the type 2, SUBCLAUSE/ADVERBIAL + MAIN CLAUSE.

Daha önceki çalışmaları incelemedikleri sürece iyi bir proje hazırlamaları imkansız görünüyor. 

And yes daha önceki çalışmaları incelemedikleri is a sentence, why not? There is a subject and a predicate, and even an object. But it is a subordinated (embedded) sentence. The marking of subordination in Turkish is DIK. You can make any sentence a constituent of another sentence (here adverbial) after you have marked it with DIK.

Two sentences are connected with a conjunction, one of the sentences syntactically governs the other.