Changing that much water will not cause your fish to go into shock and die within minutes. Even if changing all that water got rid of a good portion of your beneficial bacteria, it will not ever cause the fish to outright die in seconds. And by the way, the bacteria lives in the filter and...
A varied diet is best. A staple food of tropical flakes (or crisps which are new and less likely to cloud water) would be best with some treats in there a few times a week will help keep your fish happy and healthy. Treats could include frozen or freeze-dried bloodworms or brine shrimp...
Using your old tank water is a great idea, and it will definitely begin the process of establishing your new larger tank. Also, hooking your old filter to your new tank (in addition to the new bigger one) with your old cartridges in it will help a ton as well. Your beneficial bacteria live in...
First I would throw in a couple more neons. Neon tetras are schooling fish, which means they prefer to be in groups of three or more. Adding only one more will make them less stressed, and it will probably make their colors brighter. As far as other fish to put in there, you can do other...