What a beautiful Nepenthes! I think it is just natural leaf die off and humidity issues. You can just try to spray those pitchers as often as you can. I still do not recommend fertilizers. It is easier to kill them off with incorrect application of fertilizers. You have it growing indoors where it does not get the natural benefit of rain showers outdoors, so the concentration of fertilizer will not be washed off easily.
Yes, you can just cut-off the dead pitchers. How long have you acquired your plant?
