I cannot hear my VT50's fans unless I put my ear up to the back panel. Mine is sitting on a stand, not wall-mounted. (It occurs to me that wall-mounting could exaggerate the sounds.)
As for buzzing, I can hear it on a full-screen white, but only if there is no other sound in the room and I am right next to the TV. If the picture level is not 100%, the buzzing disappears. If I am actually watching TV (with sound), rather than playing test patterns with the speakers off, I hear no sounds from the TV itself.