R + S turns into an SH-like sound in all cases, even across word boundaries. Think of it like the way that a T + Y like when someone says "tyoosday" for Tuesday, it usually becomes a CH sound "chewsday". This happens across word boundaries as well; "Gotcha" for got you, or Anakin Skywalker's "I HAY CHEW" at the end of Episode III (he actually said "I hate you")
Sin is referring to en words, and sitt - to ett words.
Coffee (or tea) can be both, depending on context.
I think it roughly resembles English: a coffee VS coffee.
En kaffe = en kopp kaffe = a cup of coffee.
Ett kaffe = coffee.
I would use "en kaffe" when ordering a coffee, but "ett kaffe" when saying how much I love coffee :P
In this sentence, you have to use "sitt" because kaffe is an ett-word. And it doesn't matter if it's a woman in so far as you could just as easily say "Mannen dricker sitt kaffe" - as long as the subject stays in 3rd person singular (he, she, it) and the object is a singular ett-word, you can use "sitt".
Hans, hennes, dess, and deras are the same for en-words, ett-words, and plurals.