The pitchers are dead so cut off the tendrils where they join to the leaf. Some folks do give their neps a light spray with dilute fertilizer. It is early enough in the summer for new leaves and pitchers to form. If you have windowsills you can try them there. You can also summer them outside -- bright shade works well. Do not allow the media to dry out. If outside, the pitchers will catch bugs on their own making fertilizing unnecessary during that time.

I would acclimate and put them outside for the summer months. Bring them inside for the winter months.

You can cut off the dead brown pitchers. They don't hurt the plant to stay on the leaf but just in case if you don't like how it looks, it's OK to trim them off.

The leaves still have lots of green so I would leave them alone to keep photosynthesizing for the plant.

Cut the dead pitchers off, place in bright light OUT of direct Sun. Keep moist at all times, never let dry out.

also those pots should have drainage, even though they like to stay moist, they don't like to sit in soggy soil