(1)∵Three singers A, B, and C enter the championship, runner-up, and third-place finals of "I Am a Singer".

∴The probability of A being the first to appear is 13;

(2) ∵The appearance situations are: A, B, C, A, C, B, B, A, C, B, C, A, C, A, B, C, B, A*** 6 situations,

∴The situations where A comes out first than B are: A, B, C, A, C, B, C, A, B.

∴The probability that A comes out before B is: 36=12.