Setting Parameter Limits, Fixing Parameters and Their effects on fitting

I think you should start to play with some “well-defined” histograms. That means running a simple, dedicated simulation (a “toy MC”) at least several times. Each time you run it, it will create a slightly different histogram, so you will get a “feeling” of how the fitting procedure behaves, as the “exact” parameters’ values will always be the same (and known, of course).