Hi,
If you are describing about Parallels " || " icon on the Mac menu bar, yes, you can remove it by clicking on > Parallels Icon > Preferences > General > Uncheck Parallels menu : Show Parallels icon in menu bar. We can not make it appear/disappear using a keyboard shortcuts.
We can not move the Parallels " || " icon on Mac menu bar, you can move menu bar icons by holding the Command button down on your keyboard, and then drag and drop the icons into the order. You won’t be able to move the Notification Center or Spotlight icons, or third-party icons, but the rest of them–like the Bluetooth or the Wi-Fi icons–can be rearranged.