With regard to nickel strings...
Stainless steel strings have stainless steel wraps around a high carbon steel core. Your pickups will hear the core regardless of whether the wrap wire is ferrous at all. You make stainless steel by creating an alloy of iron with chromium and nickel. As you add more chromium and nickel, the alloy becomes less magnetic. The stainless steel in a kitchen knife is relatively low and is magnetic; as your kids know, the stainless on your refrigerator door is high in chromium content and non-magnetic. You'd have to unwind a string and test the wrap wire, but I would guess that they're using a magnetic stainless there.
Usually, when you're talking about nickel strings, they are nickel plated stainless steel (this is like a D'Addario or DR), so the same behavior should be seen - you can definitely pick up the core wire, probably the wraps as well.
You can buy pure nickel wrapped strings (more common for guitar, but Fender makes them for bass) where the wrap wires are totally non-magnetic, but the core wire still is seen.
The core wire is a special super-strong, high-carbon steel that's made very precisely in size. I was doing some research on this years ago and spoke to a nice fellow at the Mapes Wire Company who manufactures wire for most of the big string makers. In addition to many sizes of musical wire, they also are the big military provider for the wire in wire-guided-missiles (this is a missile where guidance information is being sent through a wire which is trailed out behind the missile!).
The reason for all this metallurgy is almost kind of silly. Your frets are nickel-silver which is basically hardened nickel. Back in the old days (the 60's) strings were pure nickel wrapped and softer than the frets. When you played the strings, the frets would wear notches in the string which led to the string losing tone. In the 70's, string makers (I think Rotosound was first) started making the wrap wires stainless steel which was harder than the nickel silver frets. They didn't get cut up as much, so the strings lasted longer (of course, the fret didn't!). Because the magnetic properties were different, it was a big change in tone, which was good for some and bad for others.
David Fung
