Ok, let's take this bit by bit.
Those mesh-top lids let out all the humidity. Do you have the top of your tank covered with tin-foil? If not, you should try following these instructions to improve the humidity. Eco-earth will certainly help! You may also scatter some damp sphagnum moss around to add additional moisture.
Can you post a picture of what you're talking about? Could be a retained eye cap, could be something else. If you post a picture here people can help you determine how urgent it is you see a vet. Covering the top of the tank and increasing humidity will also help with future sheds.
Wait at least a week between feeding attemps, and even two weeks would be better.
It's not uncommon for adult BPs to go off food this time of year, but you need to rule out husbandry issues before you can assume that. Outside of the low humidity, what are conditions like in your tank? Hot side, cold side, thermostat, etc.