First of all we have to decide if the sentences are into simple present (just informative) present continuous (happening now or in a near future).
In present continuous, changing "moving away" into "leaving my house" is OK, but if we change the sentences into present, "I leave my house" is an incomplete sentence and should need dots (...) at the end
I am nearly sure that these sentences are into simple present. Because all of his requests so far describe how to go from his house to his school. And it is possible that he has just started to learn english and it is an exercise.
I thought that "I live in a street" is more common than "I live on a street". And "living on a street" can also mean actually sleeping on it like homeless people, right? Or it is just an unnecessary detail
Prepositions in English are not so simple to deal with. For most situations there are no rules to explain why using one or another.
There are also differences between British and American English.
Americans would say "on Gültekin Street" while British could use "in Gültekin Street". What I mean is that it's not necessary to "correct" the preposition for it is not wrong, OK?
On the other hand, "one who lives in the street" is the correct form for a homeless.
About the translation, therefore it should read:
"I live on Gültekin Street. I leave home (my house)..."