Congrats on your new girl - Lily is a cutie! I've never had females before, so I'm only going to answer your other questions - I'll leave the gravid questions to those more knowledgeable.
Yes, you place the plants in their pots directly in the cage. Before you do that, though, you should rinse the leaves with warm soapy water and wash all the residue off, just in case they have anything from the nursery. The easiest way is to grab a large bucket, fill it with soap and water (I always use Dawn since that's what they use to clean up oil spill animals, I guess I just feel it's safer) and dunk the plant in, leaves first and swish it around. Then, you repot the plant with organic soil, so that if any is ingested it's "healthier" for the cham. I buy small bags of river rocks, and sprinkle them over the soil so that even if the cham is shooting a cricket and misses, they will hit the rock and not get a mouthful of dirt. So far that's worked for me.
You also asked about drainage. A lot of people on here just put papertowels down, but I do things a little bit differently. I went to Home Depot and bought a plastic utility sink - it's the same width as the cage you will be getting. I leave the bottom of the cage open, and place a 5 gallon jug/carboy under the drain hole of the sink, with a PVC pipe attached to the hole, leading into the jug. Then, I attach the cage to the sink using plastic zip ties, so that it doesn't accidentally get knocked over. Bear in mind that I also use an automatic mister, and have another 5 gallon carboy with fresh water. Therefore I don't have to worry about the mister running dry, and I can use the water that's run through the cage and collected in the jug at the bottom to water my plants outside, etc.
With your larger cage you'll have more room for live plants and that's what's going to up your humidity. Definitely monitor it, and I know that I have more humidity down here in Florida than I'm sure you have up there, but I think the plants might just be enough for you. Remember you want to mist your cham, but also to let the cage dry out in between mistings so that Lily doesn't get a URI. I run my mister 3 times a day for 10 minutes each time. I run it at 10AM, 2PM, and 4 PM, with lights on and off at 6AM/PM. Since Hoj is a lot closer to you geographically, than I am, you might want to ask how he mists his chams. Best of luck with Lily and I know she's going to have a great life with you!