First, let me clarify a linguistic point: Nowadays, both words "sherbet" and "sorbet" have entered the English language as loanwords. They both describe frozen desserts, and I have seen some people use them interchangeably and others making a distinction, e.g. that sorbet is dairy-free and sherbet has dairy. No matter how they are interpreted, sources about this meaning are not relevant to your question. It just so happens that the loanword's meaning has changed when entered English.
What you need is information about the word "sherbet" as understood in Turkey, not in English-speaking languages. And I am afraid that it is not a very informative word - it is a generic word for a sweet drink. I would actually go so far and translate it as "syrup" while noting that in modern Western countries, a syrup is seen as a concentrate to be diluted, while in Turkish cuisine, it is drunk straight (maybe at concentrations slightly lower than of the "simple syrup" found in classic western pastry books, but not too much lower).
Being that the word is so imprecise, there won't be a source referencing some kind of exact recipes for the drinks mentioned in that passage. Instead, you have to imagine people taking any combination of water, sugar (lots of sugar), and additional flavorful stuff, and drinking it. It is similar to a milkshake - what I throw in the blender is differnet from what my neighbour throws into the blender, and the "pistachio milkshake" I make today may have different ingredients and ratios from the one I made last week.
Dairy is not the first thing that comes to mind when thinking of sherbet, but there is also no sherbet police to prevent people from using it, so the kaymak (thick cream) was probably just added for more richness.
I wouldn't necessarily assume that the Mocha was drunk separately. Maybe it was, but maybe the specific example described was of a coffee based drink, the way people add espresso to milk to create a latte, or maybe they used a tiny bit of (brewed or ground) coffee as a flavoring. Just because it's unusual today, it doesn't mean that it has to be unusual across different cultures. Again, it wouldn't be a classic example for sherbet - the classic, purest form would be sugar and water, with maybe fruit juice as flavoring.