I once wondered if a microwave oven magnetron might make a good transmitter, for CW for EME.
I took a spectrum analyser and antenna to the kitchen and microwaved a glass of water, and I saw...
The most awful collection of strong tones, covering a large part of 2.4 to 2.5 GHz, all of them shifting up and down in frequency, rising and falling, as the water rotated.
I think the magnetron was strongly influenced by the food cavity, and the very many fast-changing modes supported there, depending on the position of the absorber. (imagine measuring the return loss of a microwave oven cavity, what a mess it would be. Remember a glass of water in a microwave oven is hardly a 1:1 SWR - it's still a terrible match and there are enormous standing waves). I've no idea what the spectrum would look like into a perfect load.
I didn't get a picture, this was before phone cameras, but I found a video that looks similar, here.
Magnetron for radio transmission, as opposed to heating, might be different. At least, with the right external cavity, they can probably be cleaned up a lot compared to the one I saw. The magnetron alone is not particularly high Q, a microwave oven one is probably happy to "whistle" at any frequency between 2.4 and 2.5 GHz, depending on the external circuit.
As for polarisation - remember the power from a magnetron is coupled out by a small slot or loop, into the waveguide. So there is no "magnetron polarisation", any more than there is "transistor polarisation" - its entirely due to the following components. If it goes into a simple rectangular waveguide and then a pyramidal horn, it will be perfectly linear, but that's just one choice.