You don't need to install it, it’s plug and play. It works with Windows, macOS, Linux, Chrome OS
You can use one FIDO key with multiple accounts, but that is not recommended. Regardless of if you're protecting one gmail account, or two - you should register multiple keys (if the service allows it). That way, if you lose your key, or it's damaged, or it's stolen, you will still have a backup key ready to use.
The applications support FIDO® U2F include but not limited to: Google, Facebook, Dropbox, GitHub, Dashlane, DUO, StrongAuth etc.
No. You can always authenticate the FIDO key with your mobile devices, but registration can only be done from a non-mobile device with Chrome and other U2F supported browsers.
When a red indicator blinks every 5 seconds a time, the FIDO key is in low power state. Charging process starts automatically when FIDO key is plugged in the USB port of the PC.