The normal way of saying would be "moralim bozuk", maybe also "moralim yok". "moral yok" is not a common usage, but it is used. And we also use usually "moralim sýfýr"

Eskiþehir is a city in Turkey

Kafasý güzel is a way of saying drunk.

So, "Drunk Eskiþehir".

Your writing is very effective. Towards the end I felt sad the more I read it.

A mixture of two

first the Turkish correction:

"sana da selam! senin basit bir öðretmen olduðuna katýlmýyorum. Gördüðüm kadarýyla çok tatlý ve güzel, zeki bir insana benziyorsun. Türkçe´ni gerçekten çok iyi kullanýyorsun. Senin zamanýnýn olmasýný cok isterdim. anlattýðýna göre kendini geliþtiren býr kiþisin, bu da cok güzel. bu arada doðum gününü þimdiden kutluyorum. erken kutlamak istedim çünkü perþembe günü iletilere bakmaya zamanýn olmaz. kiþiler tarafýndan beðenilen bir bayansýn, sana gelen yorumlarý okudukça seni tanýmayý istiyorum, sen de istersen"

and the translation:

hello to you, too! I do not agree that you are a simple teacher. As far as I  see you look like a very sweet, beautiful and smart person. You really use your Turkish very well. I wish a lot that you had time. As far as you tell, you are a person that improves herself, and that´s very nice. by the way, I congratulate your birthday from now, I wanted to congratulate early because on Thursday you won´t have time to check your messages. You are a lady who is liked by people, as I read comments for you I want to know you, is you also want.

for sure, she was depressed

your try is correct but not the Turkish sentence. maybe s/he tried to make it less complicated. it must be: Aþkým sen konuþmuyorsun benimle, neden? Senin problemin mi var?

My love, you do not talk to me, why? Do you have a problem?

moral yok->moralim yok-moralim bozuk

=> I am depressed/I am down

typo