Ques 1: I am assuming you meant to 'calculate the change in potential energy' in your question.
The water has a stored potential energy when it is at just at the top of Niagara falls. It loses the potential energy during its fall (which gets converted to kinetic energy). The total change in Potential Energy is simply calculated as
P.E. = m*g*h
= 80 * 9.8 * 50 Joules
Ques 2: When the car crashes into the wall it experiences a strong deceleration (i.e. negative acceleration) before it comes to a stop. During the acceleration the car has lost it's speed from 25m/s to zero.
The magnitude of the deceleration is = change in speed/time
a = 25/0.1 = 250m/s2
This deceleration generates a force on the car, given by
F = m*a
= 18750 N
Ques 3: This question uses conservation of momentum principle. Momentum is conserved in an isolated system (i.e. a system on which no external forces act). We can consider Judy and her Dog as one system. Since they are on a slippery surface, there is no external force (including friction). That allows us to use conservation of momentum.
Before Judy catches her dog, the total initial momentum of the two is
Pi = 72 * 0 + 15 * 3
After she catches the dog, the total mass becomes 72 + 15 = 87 Kg. The two together will move at the some speed which is greater than zero, but not equal to either the initial speed of the dog or of Judy. Let's assume the two have a speed v. The final momentum after the catch is
Pf = 87 * v
By conservation of momentum, Pi = Pf
Using this equation you can calculate v = 1.345 m/s