1-  ´Suya dalıp görünmez oluyor´

What is the meaning of that sentence ? He/she/it sinks into water and disappears from sight.

2- ´Annemin beni teskin etmesinden sonra ancak uyuyabildim´

Does ANCAK mean BARELY in that context ? I only could sleep after.../I could not sleep until...

3- ´Gözümü açtığımda üzerime bir taşın geliyor olduğunu gördüm´

This is the first time i have come across such a pattern, a verb followed by olduğnu, 

does this mean ´When i opened my eyes i saw a stone (in the process of) coming toward me´ ? Yes.

4- ´Annemin bazı masallarında anlatığı deprem olmuştu´

Does that mean, ´The earthquick, that my mom had mentioned in some of her stories, happened´Yes.

5- ´Sabahda kalmadan ben de ölüp gidecekmiş gibiydım´ 

What is the meaning of the sentence ? This one I am really not sure about. Maybe ´I felt like there was no morning left (for me) and I would also die and go.´  -  A native will help you. 

6- ´Bir taraftan bende annem ve babam gibi şehit olsaydım´ 

what does ´bir taraftan´ mean. ´in a way´ And does ´olsaydım´ mean if only ? It could mean ´if only´ but it depends on how the sentence continues (if it continues). şehit olsaydım ´I wish I would die a martyr´ OR ´if I died/had died a martyr...´.

7-´beni her sabah güzel sözlerle kahvaltıya kaldıran babamın sesi gibiydi´ 

That didn´t make sense to me, what does ´kaldıran´ mean in this context ´ It was like the voice of my father who every morning woke me up for breakfast with beautiful words.

8- ´ öğrenene kadar o defteri benim için sakladığını söyledi´ 

Till you are able to read ? Present participle + DAT ´until´ > until (someone, maybe the story teller, learns)

9- ´ Ben hiç bir şey göremiyordum eski evimizin olduğu yerde´ 

What´s the meaning of the sentence ? I could not see a thing in the place where our old house used to be.