I've never heard of a single piece of hardware that can do everything they talk about but you might be able to do some of it.
2. It scan the computer and transmits bits of information at each click of the mouse when surfing the Net.
Sounds like a keylogger/monitor
3. By the by, you accumulate a complete “mirror image” of the hard drive on your server, meaning that the user think he is in his hard drive, but in reality you are in control of the real data saved in your server.
Once you gain root access you can copy the hd, if it's linux you can use dd but I don't know how to for other OS's
The process generates two complete hard drives: One on the machine and one on your rented server. The next time the user boots up his computer, it’s actually the mirror computer that’s starting. The user is practically working on the server hard drive.
If this actually happened I'm assuming there would be some lag time!