When I finished downloading the (Zotero-5.0.96.3.dmg) installation package, double-click the package can not be completed, can only open an unrecognized file identity
The file is valid, so you'll need to figure out how to download it successfully on your computer. (And if you really mean Internet Explorer (on your Mac? on a PC?), you should upgrade to a modern browser. Internet Explorer on any system hasn't been safe to use in years.)
Sorry, there's nothing more we can tell you here. The .dmg is valid. You'll need to figure out how to download it properly and open it. There may be something on your system or network interfering with your connection. If this is a laptop, try from a different network.
But other software downloads and installs are normal