Tip #1 - ignore Petco advice (don't be rude, just don't take what they say as

. You should be doing around about a 25% water change weekly as standard practice anyway, and I very much doubt you have a nitrate "problem". Nitrate is very rarely a problem, it can be very high out of the tap in many areas.
If you meant nitrIte instead of nitrAte, then you have a big problem - adding fish is that last thing you should have done and standard weekly water changes aren't going to cut it.
Try 50% daily.
Also, do note that test strips are notoriously inaccurate, so don't rely on the results too much. If the results are bad, then yes, the water is probably bad, but they wont give you accurate readings of how bad it is.
And yes, fish can go for days without food. If you go on holiday for a week, just get someone to come in a couple of times and feed a pre-measured amount (stops them from over feeding). Adding some live plants is also good for things like tetras that are able to eat them.