That algorithm is called "Devil's algorithm" and has not yet been discovered. As far as I know the length of that algorithm is not known either. It would be mathematically beautiful if there existed an algorithm of length 43,252,003,274,489,856,000 that went through every possible position. I don't think it's known what the length of a shortest possible Devil's Algorithm is right now.
No, definitely not. It is well known that any <U,D,L,R,F,B> alg returns you to the starting state in <= 1260 repetitions. So any <U,D,L,R,F,B> alg that cycles through all possible cube positions must consist of at least 34326986725785600 moves.
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