Hi Hillaryh! - welcome!
I hate to say it but MANY lenses suffer from 'lens creep'. The pro lenses won't have this...but the consumer or prosumer lines....yup.
The noise though....that's usually a function of the camera's sensor not the lens. If you do a test with any other lens you have at the SAME APERTURE shutter speed and ISO - and lighting conditions - The resulting noise should be near identical...or identical.