First pic does look to have a bunch of lead in it.
2nd non magnetic? Maybe a rare earth material. I am not sure.
3rd if you can pull the copper out if the flex tubing then absolutely yes pull it out. Hopefully you can just bend back the ends and pull the wires.
4th Looks and sounds like degausing cable. That is the stuff that is in the back of a TV stretched over the back side of the picture tube. As far as the "thinking "it is stolen, take several pictures as you have like this showing it all together and being spread around for years. Typically my yard does a buy now ask questions later. They do not worry unless there is a report of something in the area stolen. In which case they now have your fingerprint and driver's license on file.



last. I am not sure on the magnets. There is much talk right now about rare earth materials and I think magnets fall into that category, but that is just a guess. I am going to start researching that a bit better.