I don't think you'll want to be adding sea salt. What you want to add is Aquarium Salt.
You can buy it at Walmart in the fish section for about $3.00. It lasts for months. It's sold in something that looks like a milk carton.
I don't think they make heaters that will fit inside of a 1/2 gallon. How are you planning to heat it?
You'll want to do 100% water changes daily in a 1/2 gallon unfiltered container.
You'll want to use either 1/4 of a teaspoon or 1/2 of a teaspoon of salt for the water if you're using a 1/2 gallon container.
When you do a 100% change you'll want to take the fish out, and run everything in really hot water to make sure it's clean. Then you'll want to run cool water over everything to cool it down. Then you fill the container with water that's cool (not cold), and water conditioner. Then put the heater in, plug it up, wait for it to heat then float the cup your fish is in (preferably the one you bought him/her in) during the water change in the cleaned container. You'll leave the fish for about 10 to 30 minutes to adjust to the temperature of the tank water, then you take the cup out of the tank, empty water out of the cup until it is just enough to cover the fish, then dip a little bit of tank water into the cup the betta is in. Do this every 2 or 3 minutes until the cup is almost full. then you release the fish into the container.
Oh and if you added salt you wait for it to dissolve first then mix the water with a spoon (that you previously scalded or boiled so as to avoid soap residue, then cooled down) so that the salt water isn't concentrated at the bottom of the container. The salt will usually have dissolved by the time the tank water is heated up though. :P
I didn't know if you've done a 100% water change before so I thought I'd include some instructions. =]
So how soon are you setting up the 10 gallon?
And you'll need to do two 50% changes and one 100% change in your 2 gallon each week until you move the cory cat to the 10 gallon. Unless you want to cycle the 2 gallon using the cory cat fish. Then I'd visit the cycling thread again and do the fish-in cycling method.