for a 10 gallon i think that having those two schools would be too much of a bioload, you'd probably be okay with a school of 10 or so of the neons, but the red eye tetras get to about 3 inches, a school of those in a 10 gallon would definitely be too much.
tetras are not a very difficult fish to take care of, but they are pretty sensitive to water conditions. if they are healthy, they will be pretty active and moving around the tank, they won't be hanging out in a corner or at the bottom, they'll also either come up to you when you go to the tank, or at least not hide at the back.
that's horrible about your
LFS........i definitely wouldn't buy fish from there.....
tetras do live in warm water, about 78F is best. and also, you should cycle your tank fishless. here are some links about the
nitrogen cycle and what your tank will be going through on a regular basis
http://www.fishlore.com/Articles/TheNitrogenCycle.htm http://www.fishlore.com/NitrogenCycle.htm
please dont hesitate to ask more questions, and welcome to fishlore!