How do I improve the services in the Massage Parlours for client requests?

Answer 1

You don't really. You try to match customer demand for ethnicity, and the general "hotness" of the girl according to the parlor.

Other than that, the girls may develop special skills over time, and if they do match it with the customers demand, but that is nothing you can control.

Answer 2

I think he is talking about the special services option which is a random event when you cash your parlour via the game map.

So clicking the symbol more often would lead to this event (or another), but it vanishes after some time again.