SSA is considered ambiguous because there are many different ways you can find an answer, also there is more than one answer. You can interpret the triangle differently and the way you interpret it is the way you will end up solving it.
2. Why can't we just simply apply the Law of Sines to the given information?
If you just apply the Law of Sines to a SSA problem it will only give you one answer, when you are supposed to find two. The height of the triangle will determine how many triangles you will end up with, either one or two.
3. How would you explain the Law to someone with minimal mathematical knowledge?