1. All fish have gills
2. A group of Neons need about 10 gallons to thrive
3. Cories do best in groups.
4. yes they do need a heater 76-78 degrees
5. The dwarf frog is pretty sensitive so I would get a bigger tank than that.
6. its a pretty big bioload for that size of a tank
7. it'll be pretty crowded in that little tank
I wouldn't do it.

At least not that many fish. You might be able to get a snail, and maybe the dwarf frog if you get the heater, which as far as I remember its fine to put one in an acrylic tank.