Can the system be moved?
Yes, but it needs to be in a stationary spot for the most part. If you want to pull it out once a week to use it, the fittings won't last long because of the wear and tear. Make sure it is set up on a stable surface so it doesn't topple over.
If you plan to move out of your current home and want to take it with you, you can. It is designed to be mounted on a wall or cabinet, and isn't something you have to leave behind some day.