ich vs. neon tetras

Question
hi there, I am i newcomer to fish as a hobby but i have tried to bring myself up to speed on set up and operation of our new twenty gallon Aqueon tank and filter setup with a four stage filter. We followed the recommended setup and let the water run without fish for three weeks. Then we added several neon tetras, from a local store. After a week or two and having only lost two tetra we added three Cory cats. For another week the H20 levels stayed consistent.  Being amateurs we failed to notice the store bought tetras came with an extra surprise, ich. I have been performing water quality tests at least once a week and the results are satisfactory and we have been treating them with AP pro ick treatment for scaleless fish, and followed the directions to raise water temp to 84F. This past weekend we performed a twenty percent water change and cleaning of the plants and substrate to try top remove the icklings from the tank.All the water that was added to the tank was de-chlorinated and AP stress zyme was added to the tank and allowed to run without fish for two hours. Prior to the cleaning we had lost 7 tetra and the Corys still show no sign of disease.  Now we are down to two tetra on one seems like his symptoms are getting progressively worse.
Now for my questions, Will Tetras school with other type of tetras(ie pastel, or some similar type)? How long should i wait before adding new fish I am trying to not kill my last healthy tetra from depression since now there are only two and soon to be one it seems? Is it possible for these fish to recover from Ich or is it pretty much a terminal diagnosis? I have heard several conflicting instructions on how to properly introduce non aggressive freshwater fish from the bag into the community.One final question, we have lost (not been able to actually find) two tiny tetra, is it possible that the Corys may have consumed a deceased fish since we have cleaned all the rock and hiding places have been inspected and there were no bodies?
Thank you for your time and help in advance
Steve

Answer
Your tank isn't cycled. Until you cycle your tank the ich will keep coming back and you will always lose fish.

You must have misread some info somewhere.

During that 3 week period you mentioned, you are supposed to be dosing your tank with pure ammonia every day. Then you add fish.

http://www.firsttankguide.net/cycle.php

Read that.

-Nick