Antenna's resistance: meaning and evaluation
about 2), from its definition it seems to me that the radiation resistance should depend on the space conditions (rain, humidity, temperature, presence of turbulences etc). If it is true, how can we design a correct matching network between an antenna and a transmission (since it is not a fixed value)?


That is true, but in general such things don't have much effect.  A microwave antenna in a heavy rain may see changes, but I'm not sure how much.

In general, if it's a concern, you'd establish the range of expected antenna impedances (because it won't be just the radiation resistances that change) and design a matching network that works well for anything in that range.


  how can I physically evaluate the impedance of an antenna? For instance a stylus antenna (I must connect it to a coaxial cable and so I thought that its knowledge is important to choice the correct matching network)?


You connect it to an SWR meter, or an RF impedance analyzer, and you do some test transmissions.