"valid" and "sound"...a question of consensus

Getting into it deeper, I found wiki's article quite interesting and informative
https://en.wikipedia.org/wiki/Formal_fallacy , which I backed into by reading https://en.wikipedia.org/wiki/Syllogism

From the former:

A valid argument has a correct formal structure. A valid argument is one where if the premises are true, the conclusion must be true.
A sound argument is a formally correct argument that also contains true premises.

Two questions seem pertinent
1. How do Dr. Bo's Criteria comport with the quoted points?
2. Are either sets/types of criteria closely related to "necessary and sufficient", phraseology of mathematical proof?

"Consensus" is in recognition that this is not an autogenous [sui generis] site that just popped up [old meaning: "made itself"], but was created with a purpose by a person who maintains it (Dr. Bo). Just wondering what the milieu is/will be.

Valid and Sound applies to the structure of an argument. Fallacies are problems with reasoning. So the rules for fallacies I have listed apply mostly to informal fallacies.

A valid argument is one that is free of any logical error considered independently of whether its premises are true or not. A logical error is a fallacy of one sort of another. One fallacy is enough to ruin an argument. As fallacies multiply, the argument just gets more ridiculous. If an argument contains only true premises it is also a sound argument.

In a sound argument, the set of premises is logically sufficient for the conclusion. If [all the premises] then [the conclusion].

Dr. Bo's criteria are perfectly good. "Valid" and "sound" as you defined them in a narrow way (from Wikipedia, not the best source) apply more to formal logic, while Dr. Bo's criteria apply more often to informal logic. "Formal" means that the argument is valid b/c of its form; "informal" means that the argument is good b/c of its content and reasoning patterns.