EDTA binds divalent (and trivalent) metal ions, such as Mg2+ and Ca2+, that activate some enzymes, such as DNase and some proteases. It also binds iron ions, which can catalyze oxidation reactions. So EDTA may be added to protect whatever enzyme you are going to purify from degradative reactions. However, if you are trying to purify a metalloprotein, you may want to avoid adding EDTA, because it may strip the metal ion out of your protein.

PVP binds polyphenols that are found in plants. These can oxidize and react with your protein, so PVP is added to prevent that.

For your first question I totally agree with Mr. Shapiro. For the second one, it will depent of your extract and plant species. content of phenols etc.. it is also important on APX extraction buffer the use of ascorbate to maintain the protein stability.

[1] Y. Nakano, K. Asada, Hydrogen peroxide is scavenged by ascorbato specific peroxidase in spinach chloroplasts, Plant Cell Physiol. 22 (1981) 867–880.

[1] K. AMAKO, K.; CHEN, G.X.; ASADA, Separate assays specific for ascorbate peroxidase and guaiacol peroxidase and for the chloroplastic and cytosolic isozymes of ascorbate peroxidase in plants, Plant Cell Physiol. 35 (1994) 497–504.

PVP (and ion exchange resins) are used to remove phenolics from your original sample. Phenolics will bind to your enzymes and can change the activity of the enzyme. Perhaps the best explanation goes back to work published by David Loomis many years ago. W. D. Loomis, “Overcoming problems of phenolics and quinones in the isolation of plant enzymes and organelles” Methods in Enzymology, Volume 31, 1974, Pages 528-544 https://doi.org/10.1016/0076-6879(74)31057-9 

Note that there is some confusion (not in the Loomis paper) about PVP and PVPP. PVP is polyvinylpyrrolidone. PVPP is polyvinylpolypyrrolidone (sometimes poly(vinylpolypyrrolidone). This is sometimes called "insoluble PVP". It has CAS Number 25249-54-1 (although SigmaAldrich lists it incorrectly as 9003-39-8). 

PVP is polyvinylpyrrolidone (sometimes called povidone). It is (correctly) CAS Number 9003-39-8. It is water soluble.

See the Wikipedia pages for polyvinylpyrrolidone and polyvinylpolypyrrolidone.

Depending on the workflow you are using, you may find PVPP preferable to PVP since it can be filtered out of solution. On the other hand, it is difficult to remove all the soluble PVP from an aqueous solution.