Usually HF is good at letting you return/replace stuff that is not working,
you may want to give it a try.
For that $7 turning set, I don't know. I have a HF wooden-handled chisel
set, it's cheap, but the chisels (especially the wider one -- 1") won't hold
an edge. They might be good candidate if I want to learn hardening them
myself.
Regards.
Pinwu