First, I'm sorry for your losses! I totally understand the frustration you must be feeling...so lets just take a step back for a second.
...to lower ammonia, nitrites or nitrates in the tank immediately...you do water changes. Its as simple as that.
What you are running into is "the cycle". Have you read up on our cycling threads? During a tank's initial "set up" period (we refer to it as the cycle or cycling) your ammonia levels will go up, then they will start to fall and your nitrite levels will go up and then fall as your nitrate rises. Nitrate is the end product of the nitrogen cycle, which is what all of our tanks are going through every day, and we remove the excess nitrates from our tanks through regular water changes. When you're cycling a tank, its necessary to monitor the levels of ammonia and then nitrites to be sure they don't get too high because they will stress your fish out. Many don't like fish-in cycles, so a "new" way of cycling is to do it artificially by adding ammonia to the tank manually instead of putting fish in there as your original store suggested the danios for.
Instead of bringing water samples to your stores and asking them to do the tests, I'd suggest getting an ammonia, a nitrite and a nitrate test kit. That way you can do the tests at home and know that you did them right. The aquarium pharmaceuticals test kits that have test tubes and droppers are good and available in most stores.
Also, its definitely not recommended to add any fish while cycling because you'll put the tank on overload. Your filter doesn't have the necessary biological materials (bacteria) to handle converting ammonia to nitrites and then nitrites to nitrates.
How many fish do you have left?
ETA: Oh and on the danios, they are voracious eaters
always will be. You just need to do your best to make sure everyone gets some, but in the end, if all of the food you're putting in is getting eaten I think that the fish store person was incorrect that you are overfeeding. Accumulation of uneaten food CAN cause water quality issues, but I think in your case it is probably just the tank cycling.