for screen enclosure best is absolutely nothing. Paper towel and news paper sticks to the bottom badly. Having nothing lets the bottom dry up faster and cleaning poop off it is super easy.
Chameleons are born hunters and free range works just fine. You can even cup feed or hand feed if you want. I love hand feeding as it's a good way to build trust with your chameleon.
Most Home Depots carry tropical plants that are safe for chameleons year round. A room humidifier and a space heater are what I use to keep my chameleons room at desired levels.
Has she ever laid for you before? How long has she been protruding from the vent for? Some of your answers are too vague and more info is needed to better help you. How many insects do you feed? Are you dusting with plain calcium every feeding or only calcium+d3 once a week?