Correct! Let me give you my full explanation:
No arms I provide, no rest
I'm an option in between
As you said, the place doesn't provide arms or rest, but directly above is a resting place, and directly below is a weapon shop, rendering the room an "option in between arms and rest".
I will put you to a test
in favour of the green
You are asked to explain the basics of the green to those who are "green", i.e. beginners.
But I'll help you too, don't fret!
A heaven's grant might be of use
At one spot, a chest containing an Ether drops down, seemingly from the sky.
Aggregate power you will get
This indeed refers to the All materia you can get. "Aggregate" is a one-word description of the kind of power the All materia gives you.
You haven't got much to lose!
Well, for one, there is really nothing to lose, except time. Moreover, this is a hint at the early point in the game. You don't have much items and the like yet.
So come on, warrior, heed the call!
"Heed the call" is a reference to the message the weapon shop man gives you via Tifa, a "call" to come there. "Warrior" is a minor hint, just a reference to how the beginners refer to you mainly as "SOLDIER".
Though you by coming here
before death's peace build thrice a wall
Remember how, in Junon, you can find another room like this? In there are the "ghosts" of the three workers found in the original Beginner's Hall. If you talk to them, they tell you something like "your explanations were so complicated I couldn't return to the planet". Therefore you "build thrice a wall before death's peace" by coming to the original Beginner's Hall.
there is no need to fear.
As I said earlier, this line is not very substantial, it's mostly an affirmation to "you haven't got much to lose", and for filling up.
Your go!
Hyperion4444, I'm sorry if you didn't enjoy the riddle, but there's no need to be rude about it. This is how I write riddles and it is as right as any other way.