Question

Wanted to understand the physics behind usage of passive antennae and matched load combination, to absorb, control and reduce the Electromagnetic-Field (s.a. due to microwave radiation from cellular phone towers), within a confined area (s.a. a room). Also, does the shape / size / material used for the antenna have a role to play ? If this kind of absorption does work, what might be the range / shape of the area that such a device can reduce / remove the radiation from ?

I have come across EMF shielding/reduction solutions which use such combination, and also some sort of Faraday-cage effect to keep out EMF radiation, which require "grounding". Are these two based on similar / related principles ?

Finally, I read in an article that not grounding the Faraday-cage (or the metallic protective shield), results in the metal starting to becoming radioactive, or maybe even emit X-rays.

Please do excuse the rather layman approach to the questions, a dumbed-down but factual (i.e. can be backed by theory and empirical data, if required) explanation would be highly appreciated.

Answer 1

X-rays

In order to make metal radioactive one have to turn it into another element or isotope. This can be performed only with high-energy particles (including photons).

X-rays can be produces if an electron enters metal with very high speed in two ways:

deceleration radiation (Bremsstrahlung)
an atom absorbs part of the electron's kinetic energy, moves to one of the excited states and moves back to ground state emitting a high-energy photon

In any case the energy of the incident radiation (or particles) must be comparable to the energy of X-ray or gamma photons. This is far from cellular phone frequency range for sure.
Shields and cages

Solid metallic shield reflects electromagnetic waves back. The material of the shield is important since it should have good conductivity. Most of metals works well. As far as I know, copper and gold are the best especially for high frequencies (microwaves).

If the frequency is quite low there is no need for solid shield.
The effective area that reflects the wave is proportional to , where ? is the wavelength.
It can be much larger than the antenna size. So metallic lattice works well if the distance between the wires is lower than ?.
GSM phones uses frequencies about 1 GHz which corresponds to ?? 30 cm.

For low frequencies the diffraction effects are important. If the size of the shield is comparable to ? the radiation can just bypass the obstacle as it happens with sound. In this case metallic box is the best solution. It can be a cage with appropriate cell size. There should be no big holes like doors and windows.
Grounding

Grounding removes charges from the outside surface of Faraday cage, but if you are inside there is no way to determine whether it is grounded or not. This is more concerned with safety.
Shape of the antenna

This is important if you need something more interesting than just screening.
Using the effect of Bragg diffraction, it is possible to build a shield that reflects one frequency and does not affect others (this will work only for some directions).
The shape of the shield also allows to control polarization of the radiation.
Edit 1. Answering the questions in the comments

Is the 'energy' of incident radiation proportional to the frequency of transmitted EMF waves, or what people commonly also call 'radiated power' measured in Watts/meter-sq (as well) ?

There are two energy characteristics for EMWs:

Intensity - the amount of energy incident on unit area per unit time (measured in W/m2). It describes total power of the radiation.
Energy of quantum - the energy of single photon (measured in Joules). It is equal to product of Planck's constant and frequency: h? or ??. This value is very important in quantum mechanics since quantum system can absorb only integer number of photons. If one photon is not enough to change system state then even 1000 photons will just pass through with no effect.

if EMF radiation that is several hundred/thousand times in excess of international norms, could cause the X-ray generation

This is possible if you have a system that can collect energy of low-frequency radiation and turns it to something else. For example, if EMW induces plasma discharge between some metallic details and electrons collect enough energy before collision there can be X-rays (I'm not sure such situation is possible).
Edit 2. Answering the questions in the comments

would the lattice structure/size computation be good enough if I base it on the highest frequency (thus get the smallest lattice size needed) ?

Also, does it matter if the material (s.a. common steel mesh) has the cross-over joints fused or insulated from each other ?

If lattice period is smaller than ? then it should work as a good screen.
Since you need computations and optimization it's better to ask someone who specializes in electrodynamics and antenna theory.
May be it's better to ask this as a separate question.
Edit 3. Answering the questions in the comments

is it possible to make practical application of Bragg diffraction to cause destructive interference of the EMF wave, when the waves are for large no. of different carrier waves, and clustered around 4-5 group of central frequencies ?

This can be done with multiple Bragg mirrors one for each frequency. AFAIK it is done for infrared radiation.

Apart from Bragg diffraction are there other ways in which the EMF can be reduced / nullified in a small region (say within a radius of 5-6 meters), where the EMF energy is captured using an antenna, converted to electrical energy, and converted to heat/light

Single antenna affects EMF only within ? distance. 5 meters is too much for 1 GHz which corresponds to ?? 30 cm.