1) Sound is heard because it is an acoustic excitation -- you modulate the pressure of the air using your voice (or whatever makes the sound), and that is carried as a wave, which the modulated air pressure vibrates your ear drum. Electromagnetic waves don't vibrate your ear drum and you therefore can't hear them.
2) Answered in the initial premise. Other examples of signals are all over computers -- your keyboard sends electrical signals to the computer to tell it which keys you are pressing, your computer sends signals to servers to request web pages, etc. A signal is anything that carries information.
3) The noise is actually mostly from heat, which makes the electrons move around randomly. This noise is actually on top of what comes in on the radio, but the radio does automatic gain control which, if the signal is too low, will boost the noise level until the signal is high enough, and if there is no real signal then the noise comes in as loud as a real signal.
4) Radio waves are electromagnetic waves, just like light except that light is a much higher frequency. They travel by creating collapsing and expanding electric and magnetic fields in their path. Sound waves are pressure waves, they move by pushing the air (or a string, drum, or something other matter) back and forth. In empty space, there is nothing for the wave to push back and forth and it will therefore not move through.