An "IT" problem is an "information technology" problem. Or easier said, a "computer system problem."
I don't know what the problem is in your case, but I also tried to renew my residence permit using the Turkish government system. I was also unsuccessful.
So I went in person to the Directorate General of Migration Management (DGMM) [or Göç İdaresi]). I gave my information to one of their immigration specialists there, and she got on her computer and did it for me.
Of course I still needed to mail my documents to the Antalya DGMM, even though I was there standing in front of an immigration specialist.
In Istanbul, life is bit expensive than other cities.
One bread near my home ( not in central district) cost 1.15 lira
Beef for beefsteak near 50 to 60 lira kg
Tomatoes 3 to 5 liras.
For hair dresser you can find cheap ones if you don't go modern and places for expat. I pay 20 liras for cut and brush
For transportation, one ticket cost 2.30 lira and price discrease if you change line within 2 hours. You buy card near 6 liras and after you put money in it.
Taxis are little bit expensive so i don't yse them often.
For home,it is really depends where you live. I advice you to have look on website previous done to have an idea