Sugar – How to tint powdered sugar (icing sugar)

A simple alternative would be to make a ganache flavored with Frangelico or another hazelnut liqueur. This has the advantage of having much less sugar, and probably better overall flavor, than an even-more-sweetened Nutella, assuming you start with a reasonably dark chocolate. All you do is boil cream, and pour it over a similar quantity by weight of chopped chocolate, into which you've added a healthy splash of hazelnut liqueur (or the liqueur can go into the cream as you bring it to a boil; either way works in my experience). Then stir vigorously until all the chocolate is smoothed out. You can pour it over while the mixture is still moderately warm and refrigerate it with the cheesecake. It will not be Nutella, but from experience it will be good, and evoke the same basic flavors.

Alternatively, most cheesecakes I am familiar with aren't topped with an icing, but a mixture of say cream or sour cream and other ingredients, sometimes added in the last few minutes of baking. These usually spread out reasonably well. You could consider softening the nutella in the microwave and mixing with a bit of cream, which will be a sort of less heavy ganache.

First, I don't know where you people all get these gelatin-filled Turkish delight recipes. Turkish delight is made with starch, not gelatin (at least the recipes used in Turkey are all with refined starch or rice flour). What you are making here is jell-o (if you use small amounts of gelatin) or gummi bears (if you use lots of gelatin).

Second, about the taste. It is normal that fresh apple juice loses its taste when it is cooked. The normal Turkish delight tastes of sugar. Its aroma comes from strong aromas added to the liquid (rose essence, or artificial aroma). You don't preserve natural fruit tastes in Turkish delight. Even if you wanted to, I don't think there is a way to do it with apple juice. Some stronger tasting fruits (cherries, raspberries) could give a syrup with more taste, but are not part of traditional lokum.

Third, about the temperature. Your observation is correct, you are just evaporating the liquid. In some cases, it might be desirable to start with more liquid and evaporate, so you get more concentrated aroma - for example, if you have started with pure rose water. But if you are making a recipe which requires concentrated sugar syrup, it is OK to start with a ratio which creates saturated syrup at room temperature (3 parts sugar to 2 parts water) and cook until the desired consistency is reached (this is recognizable from the boiling point).

For most recipes however, you don't want a concentrated syrup. The candy hardness is defined by the amount of starch used. In this case, you just mix everything and you are ready after it has bubbled, just like any pudding. The amount of sugar seems to be 1 part sugar to 2 parts water.