False bottoms or drainage layers are normally used in vivariums to raise the plant substrate above the maximum water line. ABFs and plants don't mix well unless you create a background of sorts and hang epiphytes from it to keep them away from frog's reach.
First thing you want to make sure is that there are no leaks from wet to dry area. Otherwise your dry side will become a bacteria breeding bog; drainage layer or not. Second, have to consider the ABF digging abilities and ensure the plastic window screen between lecca and shredded coco can't be dislodged by frogs activities. IMO building a false bottom with an ABG or any other large diggers is not worth the effort.
Recommend ensuring there are no leaks in your glass dam and go
with a plain bottom on dry side. Spot cleaning of poop, and a monthly substrate replacement should do for maintenance on dry side.
Paul answered your question on heating. I like to use Ceramic Heat Emitters (60W) on a dome with a dimmer. When asking opinions on a product (Jewel Neon) it helps to include a description since many of us have no idea what it is

. Good luck

!