For files to be locked when someone else has them open -- in other words to have a kind of file management feature with check-ins and check-outs, perhaps you've outgrown a simple filer's feature set and should look to a document management tool such as Microsoft's SharePoint, the open source MindTouch or even Atlassian's Confluence. There are plenty of tools out there for that.
As for sharing those files between offices, you could just put the central repository in the main office and let the inter-office VPN be the sole means of accessing the files. Beware, users will quite naturally want to save things locally. That's where some kind of check-in / check-out system will be necessary to make a new workflow for folks who want to edit and save files. Perhaps Server 2008 R2's "Branch Office" feature could help you with seamlessly caching and syncing local and remote files. Not sure if that integrates well with sharepoint though. Sorry to be ambiguous.
Backups, that's yet another topic. Either which way you go, you'll need to invest in a third party tool to perform the backups. If you want to use "the cloud" to store your stuff in, perhaps Jungle Disk's Server software will work for you. Or you could get a backup system in place that dumps that backup to a place on the filesystem which in turn gets consumed by an agent that files things in the cloud. Or perhaps you could use a tool that mounts an Amazon bucket as a drive letter and then perform all backups to that target.
In the end, you are most certainly not talking about a netbook PC with an attached USB drive. You are talking about a file server. Server grade hardware. Server grade software. (EDIT: I see now that you were joking. You'd be surprised at what is seen around here... =) ) Personally, I'd say you could build a decent filer running Windows Storage Server 2008 and Windows SharePoint Services 2010 (it's free, rolled into Windows Server) in one of your main offices. Perhaps look into deploying a smallish Windows Server running Branch Office services to remote offices as necessary. People will access the filer / SharePoint server from remote offices over the VPN. Finally, I'd use a tool that mounts an Amazon bucket as a drive letter and backup to that. There could be bandwidth issues and that could cause the backup window to be unreasonable. Perhaps you might only be able to perform a once weekly backup to "the cloud" while performing daily backups to a local repository.
And peace reigned in the land.