Ok I spotted a small mis-translation in the second paragraph.
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grubunu gerçekten çok sevdim ve harika olduğunu düşÃ¼nüyorum
Here change "grubunu" to "arkadaşlığını".
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An addition in third paragraph;
I thought you would be happy knowing he was not lonely and depressed as he was when I met him
DüşÃ¼nüyorum da, onunla karşılaştığım zamanki gibi depresyonda ve yalnız olmadığını öğrenince çok mutlu olurdun.
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and the rest is here;

İlişkimizin ilk 9 ayı boyunca (edit)benden hoşlanmadığını(edit) bilmiyordum.
NAME bana bunu hiç anlatmadı, tahminimce o hep, benimle karşılaşınca senin fikrinin değişeceğini umut etti. O hala bir ümit olduğuna inanıyor ve ben de keşke olsaydı diyorum. Benim hakkımda onaylamadığın şeyler olduğunu biliyorum, bunları değiştiremem, fakat ben iyi, dikkat eden, çalışkan ve sevecen bir insanım ve NAME için herşeyi yaparım.

Eğer bu ben kırık bir kalple yoluma devam edeceğim demekse, bunu yapacağım. Sadece keşke bize bir şans daha verseydin diyorum, çünkü sen bunu göremiyorsun ancak biz birbirimiz için çok uygunuz.
Dilerim ki bunun gerçekleşmesine izin vermezsin.

Wish the best for you Karekin,

It would be better to write in second person plural instead of second person singular, that will imply more respect to the person you are writing to. If you still didn't send the letter, I recommend changing this.

2nd person singular SEN - YOU
2nd person plural SİZ - YOU

Here are the differences on usage.
1. If you are talking to A friend, use SEN.
2. If you are talking to A foreigner, whose age is clearly LOWER than you, mostly A kid, you MAY use SEN.

3. If you are talking to MANY friends, use SİZ.
4. If you are talking to A foreigner, use SİZ (a person you don't know or just met). You may change to SEN when you feel that you became friends.
5. If you are talking to A person, whose age is clearly HIGHER than you, use SİZ, (even you have a friendship between). Excepting your family.
6. If you are talking to A person, whose social status, rank etc is HIGHER than you, use SİZ, to show your respect to his/her status.
7. If you are talking to A friend, and you feel that your friendship is not good as old days, use SİZ, to make him think about his relationship to you. A small nuance in spoken language, not in the written one.

You have to use 1 and 2 in required places. 7 is an extreme and rare usage. Always show respect to foreign people, people that you don't know. Social status, rank and your respect is very important. But if you feel that you have a close enough friendship with any people(5,6) you can also use SEN.
These are social rules of SEN and SİZ usage. In letters, if you are writing to your friend, lover, husband, wife etc use SEN. If you are writing to "a family member of your" lover, husband, wife, friend etc use SİZ to express your respect to them. You may also use SEN, if your relationship or friendship is very close to those people. But be careful, wrong usage of SEN may be rude.
In the light of above explanations, it will help translators to distinguish SEN or SİZ, which are expressed in only one word (YOU) in English, if you tell the addressee of your letter. If you don't tell the addressee, for your private reasons, it may be hard to distinguish them. Or just tell them to use SİZ, mostly everybody will translate using SEN.

You may prefer to change sen -> siz, or siz -> sen yourself.
Excepting some words that can be good to use with sen or siz, the rules is simple.
Nasılsın ? -> SEN
Nasılsınız ? -> SİZ
Senin araban. -> SEN
Sizin arabanız. -> SİZ
Change every SEN word to SİZ. And add -(i)z suffix to verbs and related words. Here -(i) can change into (ı,u,ü) depending on vowel harmony rule.

warm regards,