Since my "icon has gone missing" issue was different from the OPs, I'll add specifics for my case:
- I had been on Calibre 6.29 with Windows 10 Pro. I was experimenting with Chris Titus' Windows Utility and accidentally updated Calibre from within that. Since I didn't want to do that, I uninstalled Calibre, went to the official download page, got the official 7.4.0 version and installed that. For some unknown reason, I didn't do my normal Advanced install. Just a non-Advanced install.
- The Calibre shortcut on the Desktop and in the Start menu were fine. I was just missing the Taskbar menu (as expected with a fresh install). I added it from Start menu option, but it was nothing but a "blank page" looking icon. It worked, but it just wasn't linking to the actual Calibre icon.
- I uninstalled again and did my normal Advanced install. Everything was set to be installed, so I accepted everything. Again, the Desktop and Start shortcuts were fine, but the Taskbar icon was missing. This time, when I added the Taskbar shortcut from the Start menu, the correct Calibre icon was present.