Tarski left out some of the fine print. That "if and only if" works only under the prior assumption that "snow" designates snow, "white" designates white
Not really. If "snow" designates grass, and "white" designates green, then "'snow is white' is true if and only if snow is white" is still correct. Same if "snow" designates the sky and "white" designates green.
I'm afraid I don't understand your point.
Graham Priest discusses The Liar's Paradox for a NY Times blog. It seems that one way of solving the Liar's Paradox is defining dialethei, a true contradiction. Less Wrong, can you do what modern philosophers have failed to do and solve or successfully dissolve the Liar's Paradox? This doesn't seem nearly as hard as solving free will.
This post is a practice problem for what may become a sequence on unsolved problems in philosophy.