“Organic” can be used to label any product that contains a minimum of 95 percent organic ingredients (excluding salt and water). Up to 5 percent of the ingredients may be nonorganic agricultural products that are not commercially available as organic and/or nonagricultural products that are on the National List.1
Principal display panel: May include USDA organic seal and/or organic claim.
Information Panel: Must identify organic ingredients (e.g., organic dill) or via asterisk or other mark.
You quote a bunch of resources, and none of them support the presumption you made "lower amounts of pesticide and herbicide residues in the product, hence some tiny lessening of the probability of getting cancer. Some would also assert that the products have better nutritional values". The presumption is understandable, intuitive, but has no basis in reality.
The presumption seems to be that organic farming is closer to traditional farming and avoids practices that pollute the products and the environment. However, the government doesn't see it that way, and describes (in the resources you quote) "organic" in a way that does not require to avoid polluting practices as such, but only certain types of polluting practices... while farmers/manufacturers (obviously) compensate for them.
In particular, if we're talking about produce, then the large growers who want to satisfy the USDA Organic Label criteria of "Produce can be called organic if it’s certified to have grown on soil that had no prohibited substances applied for three years prior to harvest. Prohibited substances include most synthetic fertilizers and pesticides." achieve that by using nonsynthetic fertilizers, herbicides and pesticides in large quantities (as they're less efficient as the "default" materials). The substances replacing standard synthetic fertilizers and pesticides are not safer for humans, they're not safer for the environment, they're simply "more natural" because of arbitrary criteria.
While an organic farmer could make produce with less pesticides, that's not cost efficient, so on average mass-produced organic produce that meets all the USDA Organic Label requirements generally has more harmful herbicide and nitrate residues than the "default" non-organic produce. A friend works in food safety testing labs, and most of products that exceed the allowed limits of various unhealthy substances or are near the limits come from certified organic farms.
>achieve that by using nonsynthetic fertilizers, herbicides and pesticides in large quantities
Citation needed.
In fact, the organic program requires farmers to manage the weeds and insects using methods besides pesticides, and only allows non-routine pesticide use in the exceptional case.
>friend works in food safety testing labs, and most of products that exceed the allowed limits of various unhealthy substances or are near the limits come from certified organic farms.
This is likely due to contamination and fraud, since the letter and the spirit of the law in the United States do not permit routine use of pesticides of any type.