1. Does the Multiplication law for independent events work for more than two events?

Yes, if there are three independent events, A, B and C then P(A and and C) = P(A) x P(B) x P(C)

2. Does the Addition law for mutually exclusive events work for more than two events?

Yes, if there are three mutually exclusive events, A, B and C then P(A or or C) = P(A) + P(B) + P(C)