My try as well - but with help of Deli´s attempt 
It´s difficult for me to find sensible translation for the first sentence... I wonder if "görürsen" is actually misspelt "görürsün"? If so then maybe it can be translated as:
Beni başkalarına Bırakma görürsen (görürsün?) dayanamazsın
Don´t leave me for others - you will see, you won´t be able to bear it.
Sana ihtiyacım var; omzunda saatlerce aglayabileceğim, sonra gôz yaşlarımı silip "Ağlama aptal bak ben yanındayım" demene ihtiyacım var.
I need you. I will be able to cry for hours on your shoulder, I need to you to wipe away my tears and say "Don´t cry stupid, look, I´m with you".
(Well, maybe "stupid" is too strong word here, but apart from "fool" it´s the best translation I could find for "aptal" - not sure if "Don´t cry fool" is better translation here that "Don´t cry stupid" ?)
Biz başka severdik. O yüzden başka sevemedik..
(Not sure about it - I think it is something like this:
We used to love in different way. Because of this, we couldn´t love in another (any other?) way.
Kendini ne zannediyorsun bilmiyorum ama, ben herkesi "SEN" zannediyorum
(Sorry for clumsy translation here, but I think the meaning is something like this:
I don´t know what do you think about yourself (who do you take yourself for?), but I take everyone for you (I think that everyone is you)
- or maybe something like this - far from literal translation, but I think the meaning is similar -
I don´t know what do you think about yourself, but when I look at anyone I think I´m looking at you.
