Перевод - Турецкий-Английский - Mektubu yolladıktan sonra Istanbula gittim. Senin...

-it seems to me that the word 'aldim' is used more like for buying smthg ->
'I bought it for you and I wanted to send it to you right away/immediately.'
-'You didn't inform me/notify me, if you received my letter.'

If I'm not wrong, "take" might be used to mean to buy something. So I don't think there is a problem there. I agree with Figen on "wanted" and "right away/immediately". About the last two senteces, I think we can translate them either as they stand or by putting them together.

- Did you get my letter in your hands? You haven't told me.

- You haven't told me if you got my letter in your hands.

For fluency, I suggest the latter.

I used " right now" because of that I didn't use "past tense".

To my knowledge, both sentences are grammatical but with a different meaning.

I just want to send it to you right now. [=I wish to send it to you at the current time ]

I took it for you. I just wanted to send it to you right away. [=no sooner had I taken it than I wanted to send it to you]

Thanks all! I have edited with your comments, trying to stay close to the original translation.

With regards to 'notice'/ 'notify' - 'you did not notice'- you did not see/feel/realise you had the package (a bit unlikely...); 'you did not notify me'- you did not tell me/let me know (sounds a lot more likely!)