I am not sure what you are concerned about, but yes, you can shut off a router when you are not actually using it. There is actually a hardware device you can buy which will enable this very easily, it is called Internet Traffic Cop, and allows for easy shut off and turn on of a Wireless Router. I use it and find it very useful. It also allows me to shut down at night and cut my kids off from the net when I am not awake to monitor their activity. A great Parental Monitoriing tool.

Now, to answer you question regarding the radio signals: Yes, it transmits even when nobody is on the internet. It transmits constantly. These signals are not something which will harm a person though, so there is not worry there. Yes, microwaves are something some people need to concern themselves with, especially if they have a pace maker, or other heart equipment. Micowaves also can emit small radioactive material, which is not signicant enough for even a pregnant woman to worry herself over. Cell phones also emit very minute signals which have not been shown to cause adverse affect on individuals, even if they kept the phone to the ear for days on end. Cordless phones are even less likely to cause any harm.

However, if you are concerned by all means shut down your router when not in use. You can do so without buying the hardware I mentioned above, it is just that the hardware makes it very simple to shut down and turn on the router as needed. Just unplug the router or if it has an on/off button, hit that.

Good luck and have a very nice day.