How exactly does a basic EMF sensor work?
The ATMega168 data sheet is the primary reference to see electrical characteristics of an Analog-to-Digital input pin. Even so, the data sheet does not show some components that are probably relevant to this strange application. In the OP's source document, no claims are made for what kind of input signals might evoke a change in the ADC result.
In answer to your question2: The 10k resistor between Analog input pin and GND likely dominates, providing a digital ADC result near zero. A higher value than 10k will very likely increase the ADC result above zero (increased signal sensitivity), but will decrease intensity of the connected LED.
The ADC input pins have this internal circuit (from ATMEega168 data sheet). \$I_{IL}\$ is likely leakage current - a very small value:

Not shown in this schematic is input pin protection network which includes diode clamps to prevent input voltage from exceeding DC supply voltage, and exceeding GND voltage. These diodes may be important when an input pin contains radio frequency signals. Any voltage detected by these diodes is passed into the ADCn input pin. The other diode connected to the input pin is the LED...not a very effective detector of radio frequency signals.
The internal RC network filters out most radio frequency components - certainly any 2.5 GHz signals. 
The user is cautioned that internally-generated switching signals can affect the ADC result. These signals likely have a noise effect through their very close proximity to the internal analog circuitry. This noise source can be reduced (again, from ATMega168 data sheet):

21.5.2 Analog Noise Canceling Techniques Digital circuitry inside and outside the device generates EMI which might affect the
accuracy of analog measurements. If conversion accuracy is critical,
the noise level can be reduced by applying the following
techniques:

a. Keep analog signal paths as short as possible. Make sure analog tracks run over the analog ground plane, and keep them well away from
high-speed switching digital tracks.
b. The AVCC pin on the device should be connected to the digital VCC supply voltage via an LC network as shown in Figure 21-9.
c. Use the ADC noise canceler function to reduce induced noise from the CPU.
d. If any ADC [3..0] port pins are used as digital outputs, it is essential that these do not switch while a conversion is in progress.
However, using the 2-wire interface (ADC4 and ADC5) will only affect
the conversion on ADC4 and ADC5 and not the other ADC channels.


Is is possible to measure multiple frequencies?
Very unlikely. Since radio signal amplitude is detected before ADC input, frequency is unkownable. However, the short antenna favours higher-frequency radio signals over lower-frequency signals. Not a very good discriminator of frequency.
Note that an open-circuit input pin generally has a very high input resistance, limited only by leakage currents. An &quot;antenna&quot; wire connected to such a pin can be influenced by DC electric fields that change. Do ghosts exhale electric fields? A hand (perhaps connected to a charged body) waved over such a wire can change the logic state of that input pin. This is not a detector of radio signals. A 100k resistor added in series to such a wire would be a good precaution.