I can't seem to get my nougat to come out right and I don't know why
As you suggest, most nougat recipes require the sugar syrup to be brought to specific temperatures (typically "hard ball" or "soft crack" stage, see for example this page for details of the stages of cooking sugar). By that time, any water that you started out with (in your case in the form of rose water) has boiled off. Simply bringing the mixture up to a boil will not be accurate.

For repeatable results, I suggest you use an instant-read thermometer (or a sugar thermometer) to ensure your sugar syrup is at a consistent temperature. If the nougat does not set, increase the temperature next time. 

Regarding your second question: Even in your recipe, you add some of the syrup to the egg whites, to raise their temperature before adding them to the syrup. This is called 'tempering' and is common when using eggs in sweet applications with something hot. In the case of nougat, however, you can probably add the egg whites directly to the syrup, as was pointed out in a comment.