A better question might be, why do some reactions appear to be first or second order? Why would concentration matter for reaction rate?
The answer is that these reactions require a collision between two entities in the rate-determining step of the reaction, and the collisions are driven by statistics. The closer together your reacting components are, the more likely they are to collide with the amount of energy and the geometry that will make the reaction proceed.
So when wouldn't a reaction get faster if there were more molecules colliding? Here are some possibilities:
1) The reaction is occurring within a single molecule. Intramolecular reaction rates do not depend on the concentration of the reactant. If both components of the reaction are attached to the same chain, they are already as close together as they are going to get. Increasing the concentration only increases the chance that you will get an intermolecular reaction instead of an intramolecular reaction. Decompositions, cyclizations, and other types of intramolecular reactions fit into this category.
2) The reaction rate is dependent on something which is external to the molecule, but which is not coming from another molecule. This is where your photochemical reactions come in - if the rate determining step is the absorption of a photon of light to generate an activated reactant (usually a radical), then the only thing that is really going to increase the rate of the reaction is adding more light. Light isn't usually considered as a component in your rate constant.
3) The two components of your reaction are being held in a fixed geometry and close proximity by some third molecule. This is where the catalytic reactions come in. The catalytic species, for example, platinum in a catalytic hydrogenation, will absorb hydrogen and pre-stretch the H-H bond so that it is already weakened. Then it also absorbs your alkene, and the hydrogens are fixed in the appropriate positions to add across the double bond. Enzymes work the same way - the hold the reagents in a perfect geometry to complete the reaction. Adding more of either reagent doesn't increase the rate of the reaction because the reaction rate isn't being determined by random collisions - it is being determined by how well the catalyst can absorb the two reagents and bring them together.
If you think about zeroth order reactions in this way, does it help you to understand your list of questions?