I would place both in the larger tank as the water parameters will be less stressful. Have you researched fish-in cycling? Depending on where you live there should be a member that You will be able to rehome your Corydoras to. I live in Texas FYI
I also want to add that bottled water isn't recommended - it lacks some of the minerals fish need in their water. Tap water with water conditioner is much better.
And freeze-dried bloodworms are not good for a staple diet. Your going to want a good quality betta pellet food (try to avoid flakes - it's hard to portion) like omega one or new life spectrum. I use omega one and my betta loves it. :)
No. Ideally Fishless cycling is Bette as it causes minimal stress on the fish. I would recommend having all the fish in there, getting a test kit. And doing water changes when ammonia/nitrites are above 0 ppm
okay so i took his water to the petstore for the water to be tested and and they said the water was perfect. the only thing we could think of that could be wrong with it is he was accustomed to bad water conditions (before he was in a bowl with no filter) and now he is in pH shock. what would you do? should we put some of the water left over from the old bowl into the tank?