-Ben senin bu kadar güzel olduğunu bilmiyordum.

I did not know that you are (have become?) this beautiful.

-Akıllarınıza ihtiyacım var.

I need you advice.  

I dont understand the suffix -ıza. Akıl-lar-ın (posession?) but what is -ıza? 

Also, why is var added in the ending? What is its need?

-Sabahtan beri seni arıyorum,çünkü çok önemliydi.

I have been calling you since morning because it was very important.

-Hemen beni arar mısın? 

Whats arar?! Is it from aramak? If so what is the extra r?

-Hemen Gitiririm. 

The suffix? I understand gitirmek is to bring but what is the extra -ir? 

-Evde bazın yalnız kalıyor.

-Sometimes she stays at home alone.

-En kısa zamanda  oğrenmem lazım bu işi.

I have to learn this (işi?) in the shortest time.

-Ben seni dışardan gelirken gördüm.

I saw you coming from outside? Whats -rken? 

-İzin vermedi ki. O kahveye çıkınca, ben de hemen buraya geldim.

He did not give me permission ( whats ki?) . (ınca indicates future?) Whene he goes out to the cafe, I came here immediately.

-Sabah spormu yapıp.

Im doing my morning excercise? whats -my? and whats the suffix -ip?

-Çalmaşı çok zor.

This is an example where a verb is turned into a noun by adding -me/ma correct?

Working it is very hard.

-Allah analı babalı büyütsun.

No idea whatsoever of the meaning

I dont quite understand the word ordering in the following two sentences-shouldnt -mi/mı always be at the end of a question?

-Hiç uyumaz mı bu kadın?

-şimdi mi kalktın?

What do these words mean?

-Değişken (from değil?)

-özlemeşim (from özlemek?)

-Ben senin bu kadar güzel olduğunu bilmiyordum.

I did not know that you are / were (have become?) this beautiful.

-Akıllarınıza Tavsiyenize ihtiyacım var.

I need you advice.  

I dont understand the suffix -ıza. Akıl-lar-ın (posession?) but what is -ıza? 

Also, why is var added in the ending? What is its need?

Tavsiye - advice

niz is possesion suffix for 2nd person plural "Your"

e is (y)e / (y)a is dative case suffix cos in this sentence this case ending or suffix is required for the verb ihtiyacı olmak  

ihtiyacım var literal translation" I have need"

"Daha çok okumaya ihtiyacım var."  I need to read more or literal translation I have need to read (much) more.

-Hemen beni arar mısın? 

Whats arar?! Is it from aramak? If so what is the extra r?

 Yes, it is from the verb aramak ara is the stem, and "r" is suffix for 3rd person singular from aorist tense (geniş zaman).

-Hemen Getiririm. 

The suffix? I understand gitirmek is to bring but what is the extra -ir? 

This is again aorist tense suffix.

-Evde bazen yalnız kalıyor.

-Sometimes she stays at home alone.

-En kısa zamanda  öğrenmem lazım bu işi.

I have to learn this (işi?) in the shortest time.

 iş-i  cos of the verb oğrenmek, which requires direct object (accusative) case ending.

"Bunu en kısa zamanda öğrenmem lazım".

-Ben seni dışardan gelirken gördüm.

I saw you while coming from outside? Whats -rken? 

gelirken

gel stem from gelmek

ir aorist tense suffix

(i)ken means while 

*Ben ders çalışırken zil çaldı. The bell rang whille I was studing.

*İstanbul´dayken bu kitabı okudum. I read this book while I was in Istanbul.

Note: ken doesn´t obey vowel harmony.

-Çalmaşı    Çalışmak çok  zor. - Working is very hard.

This is an example where a verb is turned into a noun by adding -me/ma correct?

 By adding me/ma it is turned into verbal noun - çalışma, and then adding personal possesive -sı, makes it - his/her working.

 For example there is a lazy person and you are making comment by saying "Çalışması çok zor." It´s a slight chance for him/her to work, or literaly his or her working is very difficult.

-Allah analı babalı büyütsun.

No idea whatsoever of the meaning 

It is a saying when there is newborn baby as a blessing, means "May God make the baby grow with his mother and his father."