If i start download (for 1st NE) in firefox, i am able to download (for 2nd NE) from IE.
You should be able to open two windows/tabs in the same browser, and have them both run the applet for different files, no? Or does the server not support that?
As to uploading two files from the same applet, that of course depends on the server supporting that, too. If the server has the concept of a client session (or something similar), it may not.