Floating, seemingly harmless
Giddy, I laugh
Cocky, I want to touch
Thoughts, dangerous and hurtful
This refers to the Thought Chamber. The brains float in a container,
seemingly harmless. The next two lines were Ron's mistake of touching the brains and he got attacked by the brains, giggling at something when the Death Eater shot him a spell. And as said, the brains are highly aggressive and will attack if touched.
Everyone is here
Close but too far away
A hero falls
And joins us
This refers to the Death Chamber. Every person who died is there, they're
close but too far away for if you step into the archway, you may never come back. And that's the situation of Sirius, who fell in the veil and joined the others.
A baby, but older
A man, but younger
A bird that's both
And a lot of sand
This refers to the Time Chamber and the Death Eater that was turned to be a baby, getting younger and older again and again. For being a Time Chamber, it also had sands of time and the Time Turners were smashed during the Battle in the Department of Mysteries.
Hidden deep inside
Behind a secret door
It's full potential unknown
It's power is underestimated
Then this one is the Love Chamber or Ever-Locked Room. It's ever locked for its power is underestimated and I read that there's a fountain of Amorentia somewhere deep inside it.
Past, present, and future
Left here under dust
Warm, waiting for the right person
Will you come for us?
Ah, finally this is the Hall of Prophecy! The prophecies were made telling about either the past, present or future. No one bothered to go down there and, thus, left under dusts. When Harry touched his prophecy, it was warm to the touch, something he completely didn't expect. And as prophecies and whoever heard of it, will the person come for it and find out about their fate?
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That's it I guess. I think I got the other reasonings wrong.