"Copper containing alloy" is not the same as "copper". Copper lines *per se* do not have the burst strength to be used in automotive hydraulic brake systems unless their walls are HUGELY thicker than the common copper piping that's available in brake-line sizes in North America -- and I doubt there's any such extra-thick piping available. Copper-nickel alloys, on the other hand, make perfectly good high-strength brake lines (or "pipes").
A quick scan of FMVSS 105 does not show any specific requirement for steel, but I didn't read it closely and carefully.
Right. There are all kinds of different anticorrosion treatments and surface finishes. Terneplate is one of the more common ones, and generally isn't copper colored, but it's not the only one.