The source site I tested was an FTP site. Right-clicking the file on the FTP site and doing a simple Save As did properly set it. Using DE didn`t.
Download Express doesn`t set the file date/time from the site. Mass Downloader does this.
Regarding FTP clicks monitoring - unfortunately, the current IE integration scheme doesn`t allow to listen FTP listing clicks. We plan to change the scheme soon. The new one will support this.