Only the magnetic field. The others can generally be beamed.
An electromagnet could be buried in the ground.
That will just make it easier to beam stuff at it from distance.
Still, with enough effort, the listed external influences could perhaps be prevented or at least detected. But I'm afraid this would make the test very complicated and costly, so at this moment this is not the way I would recommend to pursue.
There are other, easier ways to design the test that will make these external influences irrelevant. For example, if you can command the voices not to manifest on selected recorders (perhaps by chanting another spell over the selected recorders), then a simple test can be arranged without any Faraday cages whatsoever: the recorders will be randomly put into an opaque box, and after the event, the records will be given to you. If you can determine which records are those that you ordered the voices not to manifest on, you win the million.
As you can see, with just a little more information about what the voices can do, a very simple test can be put together. What you should do now is think about - and perhaps tell us - what you can order the voices to do that will allow a simple test like that.
As they say in Russia... Don't divide the meat of a living bear.