A hint for 2 is that in a triangle, A = pi - B - C since A + B + C = pi. So you have to show that sin(A) = sin(pi - B - C) = sin(B + C).
(Take into account that sin(-x) = -sin(x) and sin(x + pi) = -sin(x)).
In terms of minimum and maximum values, you should look at the first and second derivatives. Have you covered derivatives in class?