H! Gunther is adorable! I was a new frog mommy just a few months ago, with an american green as my first baby as well! I've learned so much since getting my first frog and I'm gonna give you a few suggestions as far as his space and feeding. By no means am I an expert, but I do own six, happy and healthy, american greens. SO, that being said. I super duper respect your wishes to give Gunther his space, but it's a little reckless in my opinion. If you want him to have plenty of room I would invest in a large tank. A ten gallon is plenty. But, you seem to want him to have loads so you could go anywhere up from there I guess. Leaving him to run around your house? this one room? is kind of dangerous? There are some things in there that could irritate his skin or some plants or something that he shouldnt be around. Plus, without a dechlorinated water source he could get dehydrated and super sick. If I were you I would set up a tank that's to your size liking, with lots of nice climbing vines or branches and some nice coco fiber substrate. I'd give him a little water dish for him to soak in. He'll be just as comfortable, and will not be able to tell the difference between his cage and your backyard As far as feeding goes, I would put two or three in his cage at a time and just check back a few hours afterwards to see if he's eaten them. You dont want to put too many crickets in the cage with him for too long because they could bite him. I would also make it a point to dust his crickets with calcium and/or a multivitamin powder every other feeding. You can get the Fluker's variety at wal-mart and its not expensive at all. Also, If you're not gonna keep your baby in a sunny area of the house, You're going to need a little heat lamp for Gunther to keep him nice and warm. Dont forget to change his water bowl out with DECHLORINATED water pretty much every day. You can also mist the cage with a spray bottle at least twice a day to keep the humidity up. This sounds like a lot but honestly after about a week it's almost second nature! Good luck!
Autumn.