Password request for file delete Mountain Lion Server
You seem to have two opposing goals. You would like that users can freely share and modify each others files, but preventing them from deleting them by mistake.

The probably best way to achieve this is to user ACLs (Access Control Lists). ACLs allow for additional, more fine-grained permissions,  see http://support.apple.com/kb/PH8010 for some official Apple docs. In this case you would have to turn off the ignore permissions on this volume setting.

Unfortunately this is rather technical, and probably requires you to at least initially set it up with the Terminal.app, although some of this can also be done in the Server.app, but it will allow you to set up so that everybody can read and write to a directory and it's files and to prevent non-admins from deleting a file. Note: it probably will not prevent someone from destroying the file reducing it's size to zero, thereby de facto deleting the file, so do not get fooled into a false sense of security.