IANAbiologist, but not from what I can tell. the brown fat burns calories over hours, whereas the purpose of the cold shower is to produce more testosterone. (Supposedly.)
Perhaps, but Daniel Duchaine recommended it first, back in 1996 in his book Body Opus.
Actually, his recommendation was swimming in cold water, which would probably be much more effective.
Way back when I was in Boy Scouts, I tested for my lifesaving merit badge in a mountain lake in October. In my opinion, anyone who has the self-discipline to do this regularly isn't going to have any problem lowering his weight whatever method he chooses.
Yes, the cold showers are supposed to be taken on the lower neck area which triggers the brown fat.
And/or ice packs on the upper back. I did it for a while and felt like it made a difference. Then I fell asleep with an ice pack on my upper back and got a patch of mild frostbite.