do blood tests tell you every single vitamin and mineral?
I think you have to like request for a specific test to be done on the blood, they normally test for a single deficiency at a time I think... Or perhaps a group of related ones? They (doctors) won't normally test for absolutely everything I think, although I am not sure. But in theory that could happen and as far as I know it would be a reliable way to see that you were deficient or not.
This contraption you're talking about would be good! I haven't heard of something like that, I wonder how it would work, presumably you'd need to put some kind of sample into it (blood etc)