The following links could be helpful:

http://pd.chem.ucl.ac.uk/pdnn/peaks/broad.htm

http://pd.chem.ucl.ac.uk/pdnn/peaks/size.htm

BTW, the intensity change may imply texture is included

http://pd.chem.ucl.ac.uk/pdnn/inst1/texture2.htm

For the first question, the intensity means the how many X-ray photons are detected. The intensity profile you obtained contains a lot information related to the microstructure of the sample, e.x. texture, strain mentioned in the above links.

If you have succeeded in getting the calculated 2theta positions of all the peaks at the same positions of the experimental diffraction peaks then you have just determined the lattice periodicity (a, b, c, \alha, \beta, \gamma) correctly. But that is very far from to get a correct structure model and proper positional and displacement parameters. In any case that is already a very good start. Now your next job will be to find the correct background. This can be done by interpolating the background points where Bragg peaks are presumably absent. When you are happy with the background you should next try to estimate the profile parameters (usually called U,V, W) and then refine them. If you have done that successfully then you know that you are now ready for refining the scale parameter. This you can only do provided that you have good structure model and reasonable start positions and displacement parameters. This is because the intensities of the Bragg peaks depend crucially on the atomic scattering factors and the positional and displacement parameters but also on the scale factor that scales the arbitrary measured Bragg intensities into the absolute scattered intensities in electron units. There are other factors as well that have to be taken into consideration. I guess your program will automatically take care of the Lorentz and polarization factors correctly if you have given correctly the radiation (X-ray, neutron or electron) type and the wavelength. Also the multiplicity factors for powder diffraction will be taken care of automatically by all reasonable programs. You can now let the program refine the positional and displacement parameters. If that leads to a satisfactory agreement then you have already reached your goal. If not then the next thing would be to refine the parameters for preferred orientations. This is necessary when you sample is not perfectly randomly oriented. You will then hopefully get a better fit. If you use single crystal diffraction then the next culprit would be the extinction effect and you have to refine the absorption and extinction parameters. Mind that the absorption and extinction effects are usually negligible for powder diffraction with optimal particle size. If you still do not get satisfactory agreement then the structure model must be faulty somehow and must modify it and repeat the whole procedure until you get a reasonable fit of the calculated intensities with the experimentally measured intensities. The usual trouble maker is the presence of disorder and other defects. To treat them properly is the job of an expert crystallographer whose help you should seek in case of difficulty. Now to understand what exactly determines the diffraction intensities from a crystalline sample you must go to a standard crystallography book (X-ray diffraction by B.E. Warren for example) and read about the different factors that govern the intensities of the Bragg peaks. You must in any case understand the atomic scattering factors and structure factors and should know how to calculate them for a given space group.