Yes, this would actually be one of the best things you could use. Distilled water is great for fish because it has no chemicals or minerals in it to hurt the fish. You could put some Ph chemicals in it just in case to be double certain the water won't hurt your fish.
You can use distilled water for beta fish, but it is not the best type to use. If you're going to use water bought in big gallon bottles, go with the spring water. Best option is to fill a gallon jug up the day before you refill the tank and leave it in the sunshine at room temperature.
Distilled water should not be used for betta or any other type of fish as it does not contain the proper minerals fish need to live. Use bottled water meant for drinking for your betta fish or treat tap water with products meant to remove harmful chemicals from aquariums.
I believe distilled water has a lower oxygen content, in addition to a lower mineral content, than non-distilled water, so this may cause problems for your fish.
Yes, you could, but I don't know why you would want to. If you do you would not use any de-chlore product in the water the chlorine is already out of the distilled water. Also that goes for any bottled water the chlorine is already out of the water.
Distilled water cannot be used for any fish or aquarium. The distillation process removes much of the oxygen from the water, and fish need this to survive. If you put fish into distilled wwater, they will suffocate and die.