All references are in the cloud, so you don't have to worry about back-up. However, it may be a good idea to synchronize the references once in a while. This is done in Mendeley - at the bottom of the page.
Working in groups
When you have to write an assignment together, you must invite those who have to write together into a group.
This is done under Groups - Create Group
Click on Invite members and write the emails of your group members