This is pretty much the answer to 2:

math.stackexchange.com/questio

Short of it is, given r1=0.9 and r2=0.8, the correlation r3 of A to C must be somewhere in the range of 0.458 and 0.981. So we can infer upper and lower bounds of correlation but not anything precise, and the lower bound is WAY worse than r1*r2 (and maybe this is coincidence but I suspect not, the mean of the range is r1*r2)