Phantom harmonics when using cosine windows why do they appear and how to avoid them?
The magnitude and number of the lobes/harmonics is beyond my knowledge but you always obtain them when you window a signal with a finite window. No matter what windows you choose.

With some windows like the cosine family ones you have an efficient way to compute the convolution in the frequency domain, but if you compute it in the time domain the result is the same.

Hope it helps a bit