What you describe is not a bug or a defective camera.

Page 67 of your Instruction Manual covers this, and how to correct it.

Almost all digital cameras will disable zoom during movie recording because zoom motors make noise (except for the Canon S1-IS). The Z2 lets you make the choice of killing optical zoom during movie recording.

The other noises you hear are from the "Continous AutoFocus motor. This too can be turned off during movie recording.

A view of the movie mode menus can be found on page 45 of the instruction manual. Upper right corner of the page.