Putting a wet pan on hot stove top Sometimes when I finish making a recipe, I wash it and want to straight away start making a new one. I usually take care to dry the inside of the pan to prevent oil from splattering once the pan is heated, but sometimes the bottom of the pan is still wet, leading to a loud hissing sound once I put it back on the hot stove top.

Is this damaging in any way? The sound by itself sounds harmful, but I'm not sure if it really is. (To the pan or the stove top).
This is not harmful to the pan; the sound is just steam escaping from between the element and the pan body.

Good pans can be heated up to deep frying temperatures and higher; a few seconds of having water evaporated to dry the bottom of the pan will not hurt it.