-Je bois pour oublier
-Mais tu bois pour oublier quoi?
-Oublier que j’ai honte
-Que tu as honte de quoi?
-Que j’ai honte de boire
—Le Petit Prince
Roughly, “I drink to forget… to forget that I’m ashamed… I’m ashamed that I drink.” The even lines are just interrogations.
No; at no time in the discussion has the question of whether having sugar is a fast money-raiser even been in dispute.
“Shaving makes your hair grow faster!” “Why?” “Because it stimulates the growth.” – “Stimulates the growth” just means “makes it grow faster”
“Why can we see through glass?” “Because it is transparent”. – A transparent substance is one that can be seen through.
“I have the right to abortion, because the foetus is using my body for support against my will, and nothing has the right to do that” – We may agree that nothing else has the right to use your body for support against your will, but the question of whether nothing has will not be settled until we have established whether the foetus does have such a unique claim… which is the very point at issue.
My understanding of “that begs the question…”
A person makes a statement or explanation. However, that explanation either is not complete, or opens further topics that may need elaboration. “Begs the question” literally means, “I have told you that information, and you would most likely then ask this follow-up question…” or simpler, “it’s almost like I am begging you to ask me the follow-up question.”
For example…
“Fred lives in a rundown slum house, but drives a Ferrari and flies to Bermuda 4 times a year.
This begs the question, why does he not move to a better house? It’s because…” etc.
It’s a rhetorical device to bypass the pause for questions, or ensure the next step in the exposition is the direction the speaker wants to go.
I think it would be more like:
“We know the wall is made of glass because it’s transparent” assumes that glass is the only transparent material.
Same here. I’ve never heard this phrase being used in the technical sense outside of perhaps these boards and textbooks. I’m not sure when “begging the question” became the standard phrasing for “raising the question,” but I feel that it’s been common for at least a few decades.
This raises the question: Have you been paying attention… at all? 
Seriously.
From The Economist’s style guide (bolding theirs):
That’s affirming the consequent, not begging the question:
That’s not a good example. “All governments should promote free trade because otherwise protectionism will increase” is a tautology. It says, essentially “Do X, because otherwise you won’t be doing X.” It would be question-begging if it said “All governments should promote free trade because governments should avoid protectionism.”
What I was trying to get at would be more like:
Assumes that the question “What materials are transparent?” has already been asked, and that the answer is “Glass, and nothing else.”
How can you conclude (2) from (1) without some “If, then” statement? Your syllogism is incomplete.
Even if you did assume that the answer was “glass and nothing else”, then the conditional premise becomes “If transparent, then glass” and the conclusion “therefore, the wall is glass” holds, so I’m not sure what you’re getting at here.
Why are you assuming questions are being asked that aren’t in your syllogism?
That’s the whole point. You can’t conclude 2 from 1 without the missing “If, then” question. The person begging the question is pretending that X is already established, when in fact it hasn’t even been investigated yet. That’s why it’s a fallacy.
Even as a writer and editor/sub-editor, this is the only usage of the word I’ve ever actually seen.
As to "How did “begs the question” come to mean “Raises the question?”, my educated guess is something like this:
Begging for something is usually associated with “asking or imploring for something [money, assistance, favours, etc]”. So, “Begging a question” just seems to naturally imply “Asking a question so obvious that it’s practically begging to be asked”, at least IMHO.
The “traditional” usage just doesn’t seem to make a lot of sense to me, FWIW.