You could say "I'm a 25-year-old computer engineer living in Istanbul", but your example isn't unnatural at all. Repeating pronouns isn't a problem in English.

It would seem that personal pronouns are not used a lot in your native language, and you therefore feel uncomfortable using them in English? Don't be concerned - that is how English works. As already suggested,you could combine the first two sentences into one, but in the case of the three sentences in example 2 - there is no way you can leave out the pronouns and have these sentences make sense. I have the opposite problem - I am learning Japanese, and they appear to have a mild aversion to the use of personal pronouns, so I am encouraged not to use them unless absolutely necessary, or, preferably, substitute the person's name for 'you' - it feels very odd to me!

What you are saying is OK. To shorten it a bit you could say i'm 25 years old and am living in Instanbul. But like the other person said, your explanation is fine. Don't fix an unbroken radio.