Which vegetables should be washed before peeling them? Which should be washed after peeling? Which can (and should) be eaten without peeling them? What is the logic behind this?
Wash/rinse before peeling or eating the produce, especially if wanting to eat the skin (for example apples...)
It'll help reduce the risk of contaminating the flesh of the produce with residual pesticides (and other contaminants like dirt).
Some vegetables like potatoes can be rinsed after peeling to remove some of the starch, you can also rinse onions to remove some of the "raw-ness" when wanting to eat the onion raw
It depends on the final application/recipe.