You're on the right track. It looks like question e) is where you fell apart.
The total number of possible paths will be:
(No. Paths from A to C) * (No. Paths from C to D) * (No. Paths from D to B)
That being said, what happens if Jackson must pass through point P? The number of possible paths is reduced. Which term of the equation above do you think that changes?
Then, having calculated the total possible number of paths, as well as the total number of paths that could pass through P, I'm sure you'll know how to calculate the probability of passing through Point P.