What is a proof?

[Angrboda]

How to disprove a statements? - Get an individual to question the issue further.

A proof is a chain of logical consequences from premises to a conclusion
It can be refuted by proving that a premises is false
or statement X doesn't lead to statement X+1

A statement can be disproved by a contradiction inside it

No, this is the definition of a syllogism. Proof is a much broader concept.

And I suggest you look up the name Stephen Toulmin, as absorbing and embracing his ideas would likely be helpful to you in your rhetorical goals.