In a moment

In a moment
 

-Well, there's no use my telling you gentlemen what came of the Indian mutiny. After Wilson took Delhi and Sir Colin relieved Lucknow the back of the business was broken. Fresh troops came pouring in, and Nana Sahib made himself scarce over the frontier. A flying column under Colonel Greathed came round to Agra and cleared the Pandies away from it. Peace seemed to be settling upon the country, and we four were beginning to hope that the time was at hand when we might safely go off with our shares of the plunder. In a moment, however, our hopes were shattered by our being arrested as the murderers of Achmet.

1.To say FROM NOW, we can say IN A MOMENT or AFTER A MOMENT, but never A MOMENT LATER, do you agree?

2. To say FROM A CERTAIN TIME IN THE PAST, we can say AFTER A MOMENT or A MOMENT LATER, never IN A MOMENT, do you agree? If yes, why do the words IN A MOMENT are used?

In a moment in this case means suddenly. It's kind of like the way dentro de un momento may mean de repente in some cases.

Thank you, Poli. Forget that long passage.

1.To say FROM NOW, we can say IN A MOMENT/MINUTE/FEW DAYS or AFTER A MOMENT/MINUTE/FEW DAYS, but never A MOMENT/MINUTE/FEW DAYS LATER, do you agree?

Agreed, somewhat. What you said makes logical sense, but we can't bind the usage of the English language to logic.
There are people who say 'a moment later' when the point in time is NOW. For instance, a child may ask his mom for something and she could very well say something like, "And a moment later you'll ask for something more. No, you can't have that right now."

Also, 'a moment from now', etc.

Thank you, Rusty. Your answer is perfect. Apart from a moment later, can you think of a situation when we can say three weeks later/two months later when the meaning is three weeks from now etc.?

These types of phrases can be used to mean 'from now'.

"The store will open three weeks later," can mean
"The store will open three weeks from now," unless a time other than now was already established when the first sentence was said.