+Whenever I download a file from a website+
Safari Preferences allow you to set the Download folder location (normally Users/yourname/Downloads) but it won't automatically delete these items once installed or used you have to do that manually.
+open an attachment in my email+
Opening an attachment will launch the relevant application to view it but should not automatically save anything unless you tell it to. When saving use Save As and then when the Finder window opens browse to the location where you want the items saving before hitting OK
+open a file on a USB stick+
As above, opening a file does not (should not) automatically save it.
If things won't go into what you consider the 'right' location please run Disc Utility and Repair Permissions on the drive as that might be one thing preventing this.
