How Broadband Radio Frequency Meters work?
I think the first two are simple diode based envelope detectors. I'd be impressed if they manage to measure to within +/- 20dB of accuracy. The marketing material suggests that their target audience probably does not care about such a huge margin of error -- the performance expected from the device is to make the needle move when held up near a WiFi access point or microwave.

The third can be fitted with different probes and keeps the actual detection logic in the probe, which is a lot better. I'd expect most probes on offer to be simple diode based envelope detectors as well, however as you have dedicated probes for different frequency ranges, I'd expect that at least the antenna geometry to be useful, and correction factors to be applied to the output.

The basic setup is an RF amplifier to make the signal from the antenna usable, and the actual measurement circuit.

For fast response times, this is a very small diode (so reverse recovery time is small), behind which we can see the peak voltage of the input signal, minus the forward voltage of the diode. While this setup provides results quickly, it will only work over limited frequency ranges (which is why the third device you link to has different probes for different ranges).

Alternatively, there are wide range power meters that can handle DC to several GHz by dumping the energy into a resistor and measuring the temperature change. A single measurement takes about 30 seconds however, and the signal needs to be stable over the entire time.

For devices that use an antenna rather than measuring the strength of a signal in a cable, there needs to be a preamplifier that together with the measurement apparatus gives a flat frequency response. Achieving this is nontrivial, and any errors introduced here cannot be corrected in the digital domain later on because frequency information is lost during measurement.

If you are concerned about cell phone radiation, the best thing you can do is ask for more towers to be built, as the internal power management of both towers and phones will decrease the transmit power whenever possible. As signal strength decreases quadratically with distance, doubling the distance between phone and tower will make both quadruple their transmit power.

Newer towers also attempt to further focus the energy transmitted into the direction of the phone, because any energy sent in other directions is wasted at best and causes interference at worst; also, they will support newer protocols that can transmit data faster (reducing the time required for transmission) and also include better support for directionality.

Note that field strength is lowest directly above and below a tower, so if you plan to avoid RF emissions from mobile communication, having a base station on the roof is a good way to do so -- however your own phone will most likely use another station then. If you plan to use your own phone, look into setting up a picocell, which will allow any phones in the vicinity to use their lowest possible output power.