I bought a Chinese-made handheld radio with detachable antenna. I programmed it for FRS/GMRS frequencies, but its output is about 3W. Is it illegal? If it is, why and how would anyone find out?
Yes, transmitting with that kind of power is illegal. The max power you may transmit with would be 1/2 of a watt (0.5 watt - 500mw). Their are other factors that make it illegal as well such as the bandwidth you are using while transmitting, spurious emissions, not having a license to transmit on GMRS, and using a detachable antenna. The radio is also most likely not FCC approved. Their are multiple ways you could be "caught". Mainly telling others, interfering with local police / ems / other services, or by a Amateur Radio operator listening (or anyone with a scanner). You could be tracked down via RDF and fined or possibly imprisoned if purposely interfering with other services.
I do not recommend using your radio for FRS / GMRS services.