There are several ways of "Show[ing] that X1 is normally distributed with mean and variance given by (m1 + m2 , s1^2+s2^2)."

Read PlanetMath: moment generating function of the sum of independent random variables and http://www.math.umd.edu/~jjm/momentg...gfunctions.pdf (theorem 18).

Also read Sum of normally distributed random variables - Wikipedia, the free encyclopedia.

There are several approaches for "What can you say about the distribution of X2?" Note that if Y2 is a normal random variable with mean m2 and variance s2^2, then -Y2 is a normal random variable with mean -m2 and variance s2^2 .....