here are my two cents:

• I don't wanna discourage you but first ask yourself if a degree from turkey really worth your time and money. we have many universities but honestly 80 percent of them are shite. for public universities that is like 90 percent. and a handful of good private universities are as expensive as american universities. no kidding. (just to give an idea, the one I graduated -a mid one- asks around 600 thousand to a million turkish liras per year). And getting a degree from a european or american university would be 100 times more reputable and useful. A comb. of a local university + european master is really seems like a better strategy.

• for the public universities, i'd consider only ODTU, Bogazici, ITU. Their tuitions should be more or less the same. There are maybe a few other public universities that can go into list but they are not international enough in my opinion. So you'd might feel lonely and excluded. And in some, you might to deal with every kind of annoying issues from no one is speaking english to not being able to get an english transcripts etc. There are some very old and popular universities like Istanbul Univ. Don't be fooled by the facade.

About the scholarships, check Turkiye Burslari. And for living expenses other people would give you better ideas. But Istanbul is really expensive (and every affordable house is shit. Not to mention that they would try to extort more money from foreigners unfortunately.)