The difference between the binding of cAMP and phosphorylation is that the latter is a covalent modification. Covalent modifications are a different way to regulate proteins, and do not fall under the category of allosteric regulation. Allosteric regulation only occurs outside of the active site, often simply called an allosteric site. The non-covalent binding of cAMP to a region of an enzyme outside of the active site thus qualifies as allosteric regulation.

Because the inhibitor binds at the active site, it is actively competing with the ligand for access to the enzyme. This type of inhibitor displays competitive inhibition. Competitive inhibition can be overcome by adding excessive amounts of substrate. If the amount of substrate greatly out-measures the amount of inhibitor, then the substrate will still bind the enzyme very frequently and allow the reaction to proceed.

Noncompetitive inhibitors bind an enzyme at a spot that is not the active site. Uncompetitive inhibitors bind the enzyme-substrate complex, once the substrate has already entered the active site. Suicide inhibitors "kill" enzymes, typically by making permanent modifications to amino acids in the active site.

The x-intercept on a Lineweaver-Burk plot tells us the negative reciprocal of .

Because the x-intercept is less negative, this tells us that the inhibited reaction has a larger . Having a different x-intercept but the same y-intercept is characteristic of competitive inhibition. The inhibitor and the substrate are competing for the same binding site. 

Plotting the concentration of the inhibitor versus the concentration of the substrate will not give you any useful information because the reaction rate is essential in determining the type of inhibitor present.

Plotting initial reaction rate versus substrate concentration, or plotting the inverses, describes the graphical representation of Michaelis-Menten kinetics and a Lineweaver-Burk plot, respectively. Both of these are excellent methods to visually determine the type of inhibition displayed. On the graph, the line representing the inhibited enzyme will shift in predictable fashions depending on the type of inhibition. 

Noncompetitive inhibitors bind to enzymes away from the active site (allosteric) and distort it, reducing its affinity for substrate. Since they do not directly compete with substrate for enzyme binding, increasing the substrate concentration in the presence of a noncompetitive inhibitor will have no affect. While enzyme inhibitors include both organic and inorganic molecules, there is not enough information in the question stem to conclude the chemical classification of the inhibitor.

Competitive inhibitors can be overpowered by introducing excess substrate, so they do not affect the maximum rate of the enzyme. They do, however, make it so that more substrate is required in order to get the enzyme working at half of its maximum rate. As a result, competitive inhibitors act by raising the Michaelis constant of enzymes.

A noncompetitive inhibitor acts to decrease how fast the enzyme can act on substrates. It accomplishes this by lowering the maximum rate at which it can create products. Noncompetitive inhibitors do not alter the enzyme's Michaelis constant.

Once in the stomach lumen, pepsinogen finds itself in a very acidic environment. The acidic environment cleaves an amino acid sequence from pepsinogen, turning it into the active enzyme pepsin. This type of activation causes pepsin to only activate in the stomach lumen where it is needed.