I see what you did there.
I think you can make a stylistic case for not starting a sentence with a conjunction which would go something like:
A sentence should be a complete, stand alone unit of thought. Beginning a sentence witha construction means that it depends for understanding on a previous sentence. E.g. “I went to the shops. And I bought a loaf of bread.” The second sentence cannot stand alone. To be understood, it depends on the first. Breaking one idea into separate sentences makes for choppy reading and breaks up the flow of your thinking, making it harder for the reader to follow. I.e.
“Splitting one thought into pieces makes writing abrupt. And this makes it harder to follow. Or can put off readers altogether.” does (to my mind!) not read as smoothly as:
“Splitting one thought into pieces makes writing abrupt, and this makes it harder to follow or can put off readers altogether.”
On the other hand, your “breaking of the rule” above works well because the staccato effect is what you want- short sharp questions.
As so often, advice which is useful as a stylistic guideline becomes a restrictive imposition when phrased as a rule.
Not coincidentally, I suspect that a close examination of many grammatic rules would show that there are in fact really good stylistic advice, particularly for the kind of formal writing that was, in the past, essential to so much of life. Don’t use double negatives, don’t let subordinate clauses hang, make your sentences flow.
But style is matter of context and choice. And more to the point, style changes and evolves. Sticking to rules for writing developed by Victorians makes no more sense in the 21st century than sticking to Victorian rules of social etiquette, such as the working class “knowing their place”.