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he is in a 10 gallon fish tank and by his/herself.
Eventually frog will need a larger taller tank, specially if a Cuban. Tree frogs prefer height versus bottom area.
Humidity I try to keep between 70 and 80. Temp is kept between 70-80.
That should be OK; might need fine tuning once ID frog.
He has a shallow water dish and a deeper one that I also have a live plant in.
Water from a bottle could be many things; some of which are not good for frogs. Recommend using dechlorinated tap water (Seachem Prime is good dechlorinator) in the frogs water dish or for mixing into substrate. If your local water is hard, can use distilled water for misting since it leaves no watermarks; but avoid spraying the frog.
I have a flat heater set under the tank.
Heaters should not be under tanks in frogs enclosures. Reason is, that frogs burrow to cool down. Recommended enclosure temps are air temps close to where frogs "hangs out." That means the substrate temperature could be warmer than the recommended temperature. An alternate location is a tank side; but be aware the heat pad will lose heat to air surrounding it.
I also put smooth med size river rocks throughout the enclosure.
Fine as long as frog can't swallow them.
I mainly use small crickets but am not sure what else he will hunt and eat ( I saw some flightless fruit flies and considered getting some)
Crickets should be gut loaded with carrots, lettuce, and cherios. Size should be same as distance between the frog's eyes. If froglet is a baby can also offer FFs.
I use a calcium dust once a week on the crickets. Some tree frog owners culture Wax Worms and feed the emerging moths to their frogs.
If frog is a growing baby, you can add CA/D3 couple times a week and also give it some vitamins. Here are some schedules you can use:
http://www.frogforum.net/food-feeder...schedules.html.