You have asked many questions. Here are some answers:
1. For the problems of mathematics and logic, please read Gödel’s Mistake.
2. For the Vedic understanding of logic, please read Semantic Reasoning.
3. For an overview of a rational law of nature, which judges the truthfulness, righteousness, and goodness of the logical process of premise, question, and answer, read Shabda Manifesto.
You will get your answers by reading all these things.