I think it should be girmiş olmam

O kadar çabuk alıştım ki; bunun bir sebebi de role hazırlık sürecine girmiş olmam

I have adapted so quickly / got used to it so quickly , one reason for this is that I have entered the prep period for the role

Literally:

girmiş olmam = my entering i.e. one reason for this was my entering the prep period

Free:

girmiş olmam = (that) I entered (it)

I had a quick look at the site. Basically it seems you have to set up an ID (needing your TC no - Turkish ID number) and then enter to get all th information. These are the boxes on the right:

Sisteme Giriş

Great help.

The form is an on line one. You don´t print it and send it off. You have to fill it in on line.

They also say that:

* the documents that you also have to submit must be submitted to the management of the dorm between the dates shown on the web (they don´t say the dates here)

* the results of the application (both those allotted places in the dorm (yurt) and those waitlisted) will be posted on line.

Göküyüm -- is this song/poem just an imaginary event, or does it relate to something that actually happened? If so, what? who?

Definitely always call mum and dad anne and baba. I´ve never heard any Turk address their parent by their name. Even when talking about them to a third person they´d pretty much always say annem and babam.

The only exception I can give to this is a very modern educated family from Ankara where the adult children call their mum anne, but the lady´s daughter who is 6 years old doesn´t call her nan grandma or granny but calls her by her name Havoş (short for Havva).

With every rule there´s always and exception -- particularly when generalising about culture

The important thing is not finding absolute perfection, but to be able to know the value of what you have and to take ownership of it…
Don´t forget that even the most worthless thing that you have is more valuable that the most perfect thing that you don´t have. Because it belongs to you, it is yours....
For this reason you must truly know the value of everything in your life. Look into the eyes of the woman whose hand you hold and tell her how beautiful she is, tell her how important she is to you. And give thanks to Allah who gave her to you… 
Love her faults as much as you love all her good points!
Because the woman in your life is as beautiful as the amount of love that you have for her.
The more you love her, the more beautiful she becomes …

Ghostly, also they wrote görmeyebilirsin (= you may not see) wrongly as görmeye bilirsin (= you know to see). But for the sentence to make sense after the istemiyorsan it must be görmeyebilirsin

öyle çok içmişim ki

I had drunk so much that ...

or

I drunk so much!

içmişim comes from içmek - to drink. Literally it is I appear to have drunk, I seem to have drunk, or I am told I have drunk

Ccrook -- can you confirm what you meant by "are you bothered?"

The people who´ve helped you with translation have interpreted literally i.e. "are you uncomfortable about something" or "will it be a bother for you to see me".

But it´s a bit ambiguous and you could mean "do you care?" or "Are you bothered whether I come or not?" which would be "yoksa, umrunda değil mi" or something else like that.

No problem, like Valeriya it took a few goes to post it --- there seem to be some gremlins on the site today.