Climbing rapidly. 60k infected already and without knowing the numbers, I don't think they did more tests than any of the biggest european countries. Istanbul is a highly dense city also and I don't know which is his health care system but not at the same level than Spain, Italy, France and UK
Also, they have almost 4 millions of syrian refugees that I doubt they have much access to economic and health care system.
ON the other hand they have a respirators and textile manufacturers ans Istambul is probably one of the hottest and more humid areas that I had been in summer, and some studies says it reduces the spread
Deaths are hovering around a hundred per day. Not ideal but, considering the number infected, it's not exactly an alarming mortality rate. In terms of tests, it's done more than countries such as Spain, France and the UK, nations with notably higher mortality rates.
Syrians receive regular money and have access to free healthcare here, so your doubts aren't correct on that one. In fact, if they arrive at a hospital, they're to be seen before anybody else. That would have people frothing at the mouth elsewhere but they're treated pretty well. I don't know why people imagine they're just left to wander around and have no means to support themselves.
All in all, a lot of work to be done, and a population of 80 million will inevitably experience more deaths, but the health service and general public are doing a decent enough job so far.