Dear John and Matthew,
Thank you so much, I explored many different refinement scenarios following your advices in this post and I have managed to eliminate most of my doubts.
I am having an additional question regarding the John's 1b approach. After having confirmed how the 2-theta error (expected - experimental) vs 2-theta experimental plot of my Si standard looked like (something like the figure 5a from the ), I managed to successfully apply the John's th2_offset code lines keeping the fixed Si cell parameter at the value of 0.5431073nm (since the experimental temperature was about 25deg, or at least it was the temperature value that I read from the .raw file using the Eva software). After completing the Lebail fitting of the Si standard, I fixed the !zero, !step_error and !square to the refined values of:
prm !zero 0.01855_0.00152
prm !step_error -0.14595_0.03451
prm !square -0.00154_0.00028
and managed to refine the a parameter of Si to the value of 0.5431066nm, which I assume can be considered as a satisfying result.
However, I didn't additionally include the Specimen_Displacement correction in that case, was it still needed?
In my next trial I then included the Specimen_Displacement correction after fixing the previously refined !zero, !step_error and !square parameters and after the first refinement cycle, the following was retrieved:
Specimen_Displacement(@height, 0.00000`_0.00025 min -0.5 max 0.5).
Unfortunately, as soon as I have included the LVol_FWHM_CS_G_L and e0_from_Strain code lines, in the next refinement cycle the following was displayed:
Specimen_Displacement(@height, 0.00160`_0.00018 min -0.5 max 0.5)
and then during the check, a parameter of Si was refined to the value of 0.5431063nm. Maybe in this specific case the inclusion of the specimen displacement correction beside the polynomial function didn't make a significant impact on the refined unit cell parameter of Si in the end, but considering that I can't know for sure the exact value of a parameter to the accuracy of it's each decimal number (considering the st deviations, temperature variations and similar) and that zero and height displacement errors could vary from measurement to measurement, I don't feel confident to conclude based only on my refinement trials that the specimen displacement correction don't ever need to be used with the polynomial zero correction. Hence, it would really mean a lot to me to hear what you think about it & know from your experience.
I really have to emphasize once again that I am extremely grateful to you on your extensive help, no way I could have figured out everything myself following only the literature available online.
Looking forward to hearing from you.
 Stinton, Graham W., and John SO Evans. "Parametric rietveld refinement." Journal of Applied Crystallography 40.1 (2007): 87-95.