Unsolicited advice and painful comments must always be avoided. But people generally do not mean to hurt the single person; they simply don’t realize that their actions might be causing pain.
Being experienced in the issue of shadchanus, I know the overwhelming nature of a shadchan’s responsibilities. Thus, to those seeking a shidduch for their children or themselves: please be gracious to the shadchan. How? By sending a gift or expressing hakaras hatov in some way as an appreciation for his or her efforts.
As for approaching singles after davening or at a simcha, that is an individual preference. Some singles may feel overwhelmed or harassed if approached in either of these scenarios, while others may feel special and flattered. The best thing an aspiring matchmaker could do in this instance is to ask the single if that time is opportune to discuss the issue or would it be better to have the discussion at a quieter time. This method takes any possible pressure off the single.
It is my hope that all singles and shadchanim emulate your sensitivity in this realm. Hatzlachah!