1)Sometimes,I´m not sure about that. Which would I use,olduğu,or ki?
2)And,I´m not tottaly sure that I understood olduğu .. Shall I use for:
I heard what you said. - Söylediğini duydum???
If someone can,let give me more exapmles...  More examples is better...

1) Why do you hesitate?

2)Olduğu means that it/he/she is or that it/he/she was  (predicate´s tense is important)

+Ex: Hasta olduğunu biliyorum.  I know that  he is sick. "biliyorum(predicate) is present"

       Hasta olduğunu bilmiyordum.  I didn´t know that he was sick. "bilmiyordum(predicate) is past."

Söyle-dik-in-i that you say

Söyle-dik-i-n-i that he says

They look same but they are different. So you should guess which one is meant according to context.

Gittiğine üzülüyorum. I am sad that he goes.

                               I am sad that you go.

Tekrar sağ olun... So,in last expamle,you use dative,as far as I know. I am sad that he goes/you go. I didn´t understand why dative,but neber mind. I´ll learn later,it´s not too important right now. One more time,thanks..

It is dative because verb wants it.

Gittiğini duydum. I heard that you went.

Now it is acusative. It is all about which case verb wants.

Oh,I understand now.. Thank´s .