Gelen kadın kimdi? (Who was the woman that came?)

Geldiğini kadın kimdi?

arasında ne fark eder? ikisi aynı anlama geliyor mu?

başka örneğiler göstereyim, bunlar kafıma karıştırıyorlar

bunu okuduğunu genç kızı gördün mü?

ya da

bu okuyan genç kızı gördün mü?

hangisi daha doğru? ve arasından ne fark anlamalar verirler mı?

aynı zamanda

Geri dönersin diye bekliyorduk. (We were expecting that you return)

niye dönersin yazmış?

"geri dönmene (your coming back) diye bekliyorduk", neden olmasın?

The overstroken lines are not grammatical.

The AN participle is used when the constituent governing it is the grammatical subject of the main clause:

kadın geliyor/geldi > gelen kadın

kız okuyor/okudu > okuyan kız.

Notice that this holds true for the passive sentence also:

hasta bakılıyor/bakıldı > bakılan hasta.

Roughly, the DIK participle is used when the word governing the participle is the grammatical object or adverbial of the main clause.

Kız okuyor/okudu. > Kızın (GEN) okuduğunu (ACC) gördü.

Kadın geliyor/geldi. > O kadının kim olduğunu biliyor musun?

Adam şehirde yaşıyor/yaşadı. > Adamın (GEN) yaşadığı şehirde deprem oldu.

diye marks a straight quotation. That is why we don´t need to play with infinitives/participles at all when using it. 

Neredesin diye merak ediyorum.

Nerede olduğunu merak ediyorum.

Or in a manipulative sentence with infinitive:

Burada kalmasın diye istiyor

Burada kalmamasını istiyor.

Actually there are many questions in your question, raydin. Feel free to ask again if this answer was too condensed.

Thank you for the explanation I think i get it but I´m still confused on one thing, when I speak Turkish I have so much trouble with knowing when to use the an suffix and the dik particle. 

Like for example I would say something like this, 

kadının geldiğini kimdI? which I know is an improper way of saying it,  but I guess I need more practice.

Also, 

is it better to say 

onun gelmesi bekliyordum

or can you say 

onun geleceğini bekliyordum 

do they mean the same thing?

bekliyordum = I was waiting for / I was expecting

you need a object there to state what you were waiting for. so "Onun gelmesini bekliyordum" will be alright.

hmm i see now thank you guys for your help. i will have to do a bit more speaking practice with my friends to get better at knowing when to use dik particle and the an suffix. 

I hope this simplified information will help you.

-dik and -an are used to form verbal nouns (isim fiil) from verbs.

verb+dik = noun

tanı+dık = tanıdık (a person whom one knows) acquaintance

verb+an = noun

ağla+y+an = crying

This type of words are also called participle and they can behave like adjectives and modify nouns:

görül+me+dik = görülmedik (not seen or known beforehand) unforeseen

görülmedik felaket = unforeseen calamity

yat+an = yatan - lying

altında yatan = (lying under or beneath someting) underlying

erozyonun altında yatan birçok neden vardır – there are many underlying causes of erosion

Meşe, ışık isteyen bir ağaçtır – the oak is a light-demanding tree

bu hastalık insana sıtma taşıyan sivrisineklerle geçer - the disease is transmitted to man by malaria- carrying mosquitoes

I am not as highly talented linguist as Abla, nor like Tunci who is the master of Turkish Language (I love´em both), but a poor amateur, and yet hoping the following simple examples will help you to find out how -an and -dik are used in sentences.

Compare them with English relative pronouns, but keep in mind that it is not always the same way:

Sana telefon eden bendim - it was I who telephoned you

Aradığım kalem buydu - that is the pen which I was looking for

Oturduğun sokak bu mu? - is this the street on which you live?

Binmemiz gereken otobüs şu mu? - is that the bus which we must take?

İstediğin dergi bu mu? - is this the magazine which you want?

Geçen hafta seyrettiğimiz iki film de kötüydü - both movies which we saw last week were very poor.

p.s. Dear Tunci, I am so sorry for last night that Fener sent Cimbom back home with empty hands and tears in eyes.. But I think you are very used to it after all these 16 years.  

Hi Scalpel. Will you take a look at the puan. I think Cimbom is still on top. Also what they are used to.

thank you for your explanation makes perfect sense now 

Yep, still on top but this will last a week or so ( I HOPE!)  

you´re dreaming buddy!

Dear Scalpel, Don´t be sorry. Galatasaray is still most known/succesful Turkish team in Europe/World. 

tunci, my dear friend, I really appreciate GS´s past success which was before Christ.  The only thing that I remember from those days is that there hadn´t yet been removed six (6) zeroes ( from Turkish Lira. 

not: tunci usta, eskilerden si++´yi göremedim henüz. Buralarda mı? 

Well I think everything is cleared up now. 

Tebrikler to all GS fans