I cannot believe that there would be no living creature with the capability to hear sounds in a forest. As far as I am concerned the word 'no one' relates to a person, not to animals. So if there were animals in that forest, they would be there to hear the tree fall. See, when I am not home and my husband farts, does it still make a sound? Yes it does because my dog is there to hear it! On a more philosophical level, I think that the sound and the tree both exist even though they are not perceived by a human being.
No it doesn't. Sound works by air vibrations, if there is nothing like an ear drum or microphone to pick up those vibrations then it doesn't translate to sound, so it effectively silent.
There is no right answer to this, I posted it in a previous opinion as part of a topic where someone was scientifically approaching the saying about drops of water creating an ocean. It is meant to centre your mind and help you focus for meditation purposes and is not supposed to have a real answer. The same as my other one I quoted of "what is the sound of one hand clapping". Obviously from a scientific point of view a tree falling does make a noise but that is the intent of the saying but it is meant to make you think about the whole concept of what if no one is around how do you know it makes a noise and be scientifically broken up.
It would produce sound waves, but if nothing mechanical, or biologically sensory was around to process these waves into sensual form, the waves would dissipate over distance. Thereby producing no sound as we, as humans, would understand it.