Drywall – mount a projector shelf to drywall

Toggles and other heavy weight drywall anchors can be suitable for TV mounts when the mount is flush. Or toggles in to metal studs. Since the load is mostly shear and not pull-out, this is fairly safe. (Provided the drywall is thick enough, the anchors are installed correctly, the wall is properly supported, and lots of other considerations too numerous to go in to here.)

However, adjustable, articulating or arm mounts should never be used on just drywall or metal studs. No matter what anchor you use, drywall and metal studs can not handle the pull out force applied when a TV is extended or tilted away from the wall.

So either get a flush mount, or open the drywall and install appropriate wooden studs.

Just as a frame of reference, 26dB is about the sound level of a person breathing. Typically these are measured at a distance of a meter from the source. Whether or not this will be objectionable is mainly a question of personal preference (and how much other sound sources such as your speakers mask it). My suggestion would be to pick up a computer case fan with a comparable decibel rating, put it where the projector will go and see if it would be a problem for you.

As far as increasing distance goes, it will obviously help. Sound level drops by roughly 6dB for every doubling of the distance, so at 2 meters it should be barely perceptible and at 4 meters you would have to try really hard to pick it out.

Bear in mind that 26dB is the claimed decibel rating, and the actual noise level you perceive can vary depending on frequency, vibrations in whatever it's attached to, etc.