The bold marked sentences are the one I am trying to translate. First I tried to "fix" them and then I tried to translate. I would like help with corrections, please =)

k.bkmazsan biraz erkn uyuyacm olur mu

Kusura bakmazsan biraz erken uyuyacağım, olur mu?

If you do not take offence/ I am sorry I will sleep early, is that alright?

It is more like "If you never take offence, I will sleep a little earlier, OK"

snden snra çktm uyudm ki

Senden sonra çıktım. Uyudum ki

I went after you. I was (really?) sleeping.

Could be "I fled from you that I was sleeping", or like what you said.

 # When is "ki" most often used and how? I know for example "bilmiyorum ki" which is, when using the "ki", pointing out that you really do not know.

By the way, I am just a beginner so go easy on me!