For the second question
s''(0) = a
so s'(t) = at + ?
s'(0) = v
Can you take it from here?
Be careful about problem two. I would have interpreted "a= 32, v= 20, and s= 5 when t= 0" as meaning all three values are given at t= 0. In that case, you do NOT know the acceleration at any other time and cannnot answer the question. You have to assume that "a= 32" means that the acceleration is the constant 32 while v and s are given at t= 0.