I'd like to setup an ftp such that my users (and some software I write) can upload documents, and have those documents saved on the server but I don't want to allow users to see the contents of the ftp folder - essentially the ftp looks empty at all times to the user.
Sure, for example with ProFTPD you could use the following configuration:
With vsftpd you can set:
Depending on your FTP server it us usually as easy as giving someone write but not read permissions on the directory. This article discusses it briefly
We've had a client using the scheduled sweep method for years without issues. I'd only see it potentially being a problem on a heavily used server with multiple people intentionally dropping files with the same name.
Regardless, here's an excellent step by step procedure for setting up a blind drop ftp site on Windows 2003 using IIS: http://www.iisanswers.com/Blind_drop_ftp.htm
As mentioned, it's easily possible. Your best bet is to do a Google search for "(FTP server type) write permission only" and you should get plenty of responses. Without more information on exactly what FTP server you're using, you're not going to get much more help than that here.
Yes. You simply give your FTP users write only access. Lots of support sites do this for log files and the like.