What concerns the “empty bins treatment when fitting”, see [url]Empty bins treatment when fitting
In short, it is possible that a bin is “empty” but it has a non-zero error, and in this case the “chi2 method” will consider this bin (and there’s the “WW” fit option, as well), while “non-empty” bins with zero errors will NOT be considered.
Moreover, the “likelihood method” doesn’t seem to care whether bin errors are zero or non-zero (it considers all available bins in the fit).