>Is it better to continue with stacked raw images for the calibration, and to use images taken the same night? Any tips are welcome.

For highest accuracy it is best to take a calibration star on the same night and approximately the same elevation as the target, particularly if the target is low in the sky. This helps to make the atmospheric extinction similar. In practise though you should get a reasonable result  using instrument response calibrations  from  other runs. As a variable star observer you might be  interested in the effects of extinction on spectra. Christian buil has recently added a page on the ARAS website on how to correct low resolution spectra for extinction here. (It is not for the beginner though!)

http://www.astrosurf.com/aras/extinction/calcul.htm

Note that if you have used the "spectra" "correct tilt of a 2D spectra" function of IRIS to level the spectrum, this changes the X scale so the wavelength calibration of calibration star and target will only be comparable if they were both changed by the same angle. The "geometry" "rotate" function does not change the scale but can give more pronounced wave artifacts in the spectrum.

Best Regards,

Robin