1) You can only build stage plots in the mobile apps, but you can still use the website to enter notes and contact info. Basically, the apps are better for drag-and-drop and gesture operations and the website is better for data entry.
2) No, set lists are available to every user in a project. You can link a set list to an event and assign the event to specific users, but they can still browse all the set lists.
3) I use one of the best hosting companies in the business and I back up my database several times a day using two different automated systems, one hosted by the same company and one by a different company. You can make your own manual backups using the Export buttons at the bottom of the Songs, Events, Contacts and Transactions pages. Uploaded files (documents and recordings) are not backed up on my system, so you should keep your original copy of any files you upload to your account.