Larry, I have had piano lessons up until my teens and also had a dash of cello as a kid and attended a basic guitar class in Jr High. I have completely forgotten how to play the cello and guitar. I have had my theremin for almost a month now, and I am starting to play, what sound like to me anyway, songs. I have not recorded any of my playing yet or had it critiqued by anyone else, but I am definitely at that point.
As for ear and pitch skills please see my other post in the "Theremin Newcomers" forum called "What type of ear skills do I need: absolute pitch or relative pitch?". I have parked a keyboard next to my theremin. For part of my practice I like to go through the entire keyboard (it is a five octaver and exactly matches the range of the Etherwave) note by note and match it with the theremin. Then I would also hit random notes and match those too. You will get a unique humming/singing sensation when you are on the note. The keyboard comes in handy for practicing scales and arpeggios too.
I do not own a tuner. At this point I don't think I need one. For one thing, I am legally blind and have to get my face real close to printed materials, displays and such to read them. This would make it a real pain and labor intensive for me to use a tuner. I would have to bend over to read the display of the tuner thus, causing my pitch hand to move around. When I stand up my pitch hand will move again, etc.
I know it is a big investment to go out and buy a theremin, but that seems to be the only way to see if you can learn to play one or not. Although in my opinion if you are lucky enough to know of anybody that owns one maybe you should see if you can borrow it a few times or put in a few practices and/or hit them up for a couple of lessons at there place.
It seems that sometimes the only advice that is out there, concerning taking up the theremin, is: GO FOR IT!! :)