package for exploring point source effect on ilc foreground removal algorithm
First, the hesse algorithm calculate the error by calculating the hesse matrix of the log-likelihood which is the second derivative corresponding to the parameters. Therefore, the error of norm beam is just the inverse of sqrt hesse matrix, i.e. the model itself square divide by the variance of data. In different nside situation, the data point is square proportional to the nside square, but the data variance is also square proportional to the nside square. That's why the norm beam error is the same at different nside.
2. Will non-diagonal terms to CMB covariance matrix affect the parameter fitting for T map or QU maps?
From my result, it won't if TQ,TU non-diagnal terms are added for T map's parameter fitting. But QU non-diagonal terms do affect the fitting for QU maps because Q,U themselves are not good quantity.
The apodized mask will have small structure on small scale, so be carefull of it when calculating the power spectrum. The solution to avoid this is to deconvolve your map first, then estimate the power spectrum.
The theoretical band power spectrum is related with your mask choice so it is better to compare all your power spectrum with the same pipeline or the same mask rather than compare the result with full sky power spectrum estimation.