I don't have any helpful suggestions regarding site certificates/ssl etc..

are you still having trouble opening/viewing a certain type of file? I need to know what the file extention is for the file/s that you are having trouble download/uploading. The extension is the three or four charactors at the end of the file name following the "."
Some examples of common file extensions are:
".zip"
".exe"
".rar"
".xls"
".html"
".xml" etc..

If your version of windows has "hide file extensions of known types" checked, you won't see the letters for most files on the computer's drive. You'll have to uncheck hide extensions of known file types, "from the windows control panel open up "folder options" click on the "view" tabe then scroll through the menu and find the option for "hide extensions of known file types" uncheck etc... either that or or right click on the file name and select "properties" in order to see the file's extension and other information; post the information about the files so we know what to help you with..

If the file is on a remote system, you need a direct link to the file that they have uploaded, or ftp access; to browse the remote systems shared directory.