Anniegump covered the frog issue pretty well, so I'll just state that you'd best catch those frogs if you can and stick them back in the 10gal... regardless of whether you want them or not, you took them into your home and in doing so basically agreed to properly care for them and ensure their survival. By releasing them into the wild you have broken said agreement and I personally would no longer trust you with living creatures.
On to the betta. Why not keep it in the 5.5 gallon tank with some shrimp? That way you get the shrimp and the betta doesn't go into a bowl with water changes every "few days". Also, if it DOES go back into the bowl, you should do a water change every day to prevent a buildup of toxic byproducts like ammonia and nitrite/nitrates. Or have it live in a heavily planted nanotank (like a vase with plants and such, they can look very nice if you do this).
On to the puffers. As cool as they are, with your track record they would be dead or released into your pond by the end of a week. They need inverts like snails and shrimp to feed off of, and are superpoopers, meaning they need better filtration then other fish of their size. I would avoid them if I were you, until you have prooven your ability to keep high-maintenence livestock (like the frogs) alive and well in a tank.
Now for the Celestial Pearl Danios and the stocking of a 10 gallon aquarium. I think the frogs should go back into this tank, but if they don't here is what I would stock it with:
6X Celestial Pearl Danio
1X Sparkling Gouramis
Then I would plant the tank with a standard 10gal hood/light because plants seem to LOVE that amount of light for a 10gal. I would def have a filter and do 50% water changes weekly.
I hope you listen to the advice and comments people are giving you Patrick.
~Travis