Your setup looks fine. I would try to add more climbing surfaces near the top, though. Either a few branches or taller plants will do. You can also use fake vines or suction some fake plants to the glass. By adding more climbing areas to the "airspace" of the tank, you are effectively making the vivarium bigger, as your frog will be able to roam in more areas than before.

Are those plants real? If not, you don't really need a soil-like substrate at all. You can use something as simple as moistened paper towels for the ground. I'm not suggesting that you do that at this point, but it is an option in case you decide to remove the eco soil later on. Forest moss is different from sphagnum, but it should serve the same purpose of keeping in moisture and covering the dirt, keeping it from getting on the frog. It can still be an impaction risk, which is why I recommend either keeping crickets in a bowl or feeding them with a set of tongs. White's tree frogs are not shy eaters, and should not mind being fed by hand.

What is the temperature in the tank at night if you don't use the heat lamp? Whites can tolerate nighttime drops down to 65 F without issue. The reason I asked about the night/heat lamp earlier is because there's a chance you may not need it at all. How many watts is it? You mentioned that it gives off a red color. I'm not an expert on the matter but I remember reading something to the effect that not all frogs are blind to red light, and that a red night light has been known to interfere with the activity levels of certain nocturnal species of tree frogs. Basically, if your temperatures are above 65 without the night light i.e. you don't need the bulb for the heat, you should try going without it and see what happens.

As for him opening his mouth, that's most likely just normal skin shedding behavior. Most of my frogs do it every week or so. There may be other explanations...but I don't know of any...so no worries there.