Just cut it off. Leaves do die from time to time. Keep the soil always moist.

We were all newbies at one time!

I concur with Tommyr, just clip the dying leaf off and the plant will make more. The lowest leaves will die back one at a time as new leaves overgrow them and the lower vine will develop a woody outer layer to strengthen and protect it as the growth point rises.

You can sprinkle sulfur based fungicides on the soil surface or spray neem oil to kill the fungus. It proably will not harm the Nepenthes, but you can never be too careful.

I water my Nepenthes twice weekly as well. I just water till I see runoff under the pot, then remove the runoff if it is too excessive.

The pitchers producing fluid is a good sign, the plant likes your home and is getting ready to catch insects. You will likely see new pitchers start to form soon as well.