We're working on some backup and delete protection functionality that will be core to the software in a future release. Right now there are options to export your Feature Services to shp or FGDB that might be backup enough depending on your needs and goals. As for the webmap, you can always capture are reload the json but it's a bit more advanced.
Brian does have a nice tool that's available and may also suit your needs.
Yes, you can use python to automate and create backups of your content if you needed. You will have to use the httplib and the ArcGIS REST API as documented Online.
I will have a look at the Arc2box. I have only just started using Dropbox myself for work purposes, so need to familiarise myself some more with this product.