Mathematically, if your force isn't constant, then to find the energy, you need to find the area under a force/displacement graph.
Here's my take on things.
Q22: 1/2 mv^2 + 1/2 kx^2 = constant
So the relationship between KE and x should be quadratic in x; negative parabola.
Q34: as above
Q37: work, by definition, is a force acting on a distance. If your force doesn't move anything, there is no work being done. You can think of work as a change in kinetic energy. If there is no change in displacement, then your object isn't moving any faster or smaller -> no work done.
How to deal with Q36?
What is the origin of this spring force? You have bonds between atoms that make up the spring force. By using Hooke's law, we're approximating this force as being linear in the displacement, which is generally a pretty good approximation. Now, if your spring is twice as long with the same material, you have twice as many of the same identical atoms that pull on each other. The quadratic nature of the energy means that the most stable configuration is when all of the atoms are the same distance from each other (this can be proved using some version of the AM-QM inequality I think but I'm not going to go into the details here).
Now, let's look at the atomic cross section that is attached to the mass. This layer of atoms has to bear the entire weight; by Newton's third law, if it is pulling the mass up, the mass pulls this layer of atoms down. The next layer of atoms therefore has to exert a force equal to the weight force on the first layer of atoms to hold them up. Apply this logic to all of the layers of atoms there and you'll find that the extension = number of layers * extension between layers
Double the length of the spring -> double the number of layers of atoms -> double the total extension