So basically, this is the question.
I guess "Senden önce" means "before you", but what is "Senden öncesi"? Is öncesi a noun in this context?
I asked a Turkish friend of mine, but he couldn´t tell the difference. Thanks in advance!

                   senden önce ´before you´  -  ADVERB

                   senden öncesi ´the time before you´  -  NOUN

The sg 3rd possessive suffix does these tricks. The same way about place:

                   Dışarısı/burası soğuk. ´It is cold outside/in this place.´

The use of the Turkish sg 3rd possessive suffix is quite idiosyncratic. In general it seems to have a limiting function. Here it is distinguishing a certain slice of eternity, its time and place.

Another one ;

Sonrası -à After of something.

Senden sonra  -à After you

Senden sonrası ---> The time after you