Can I track a device...

...if it's off or without an internet connection?

Unfortunately, there is no way to monitor a device if it is unable to send data, so it's vital that it’s on and connected to internet. We are aware this may sound like a big push-back, but it's the minimum requirement any similar agent needs.  

...with the phone number, serial number, IMEI or others?

That’s not possible. This information doesn't provide a location and the device wouldn’t be able to connect with our Prey servers. Also, it could conflict with laws about spying and privacy.

...if the app was not installed prior to the loss or theft?

No. Prey can only help you in case it's already installed and configured on your devices, before the worst happens. If it isn't, then the app won’t be able to render any result. This is not limited to Prey only, but it applies to every tracking application out there.