What do you consider a "very light version" of embedded Linux? Qt needs a framebuffer (linuxfb, directfb or similar) to be able to show its UI somewhere, as for the rest it really depends which parts of Qt functionality you need, surely a bunch of libraries will be needed as well.
As for the second question, Qt needs some drivers and libraries. You'd have to provide them all in a single large blob to be able to even think about running it without an operating system.
You could go for any U*ix system that is not Linux (e.g. QNX) but I don't really see what benefits it might bring you. I think you should first answer my initial question.
About licencing costs -- if you can use Qt LGPL then you don't have to pay anything. If not (as for "running Qt without an operating system") then unless your software is LGPL-compatible by itself, you'll surely need a commercial licence.
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