Touch sound and vibration are enabled when using the default settings on the Sony Xperia Z3 (and Xperia Z3 compact). To disable and turn off touch sound on Xperia Z3 as well as the vibration feedback, do as follows:
1. Open Settings and go the Sound settings
2. Under the System settings, make sure to unmark the "Touch Sound" option to disable the sound when touching the screen
3. To disable vibration feedback when touching, unmark the "Vibrate on Touch" option
4. There is also the "Dialpad touch tones" option which is to specify whether the touch tone should be enabled when dialing or not.