1) In mathematics, a hemisphere is a 3D shape with one curved side and one flat circular side.
Agreed.
The flat side is the floor.
Not necessarily, it does not say so in the description. And although the dome needs to be "above", nothing says that it can't be cast at an angle like a shield.
2) If it didn’t have the flat side, how does the volume within the space stay comfortable and dry despite the conditions outside?
Because it's magic and the effect within the hemisphere drys the air and keep it comfortable, it says it clearly: "The atmosphere inside the space is comfortable and dry, regardless of the weather outside."
a) If it was a sustained downpour for even a short duration, the floorless structure you propose would suffer groundwater seepage due to lack of a vapor/moisture barrier. The area inside would cease to be dry.
It only says that "
the atmosphere" inside is comfortable and dry regardless of whether, but if it's flooded by something which is not atmosphere (water, lava, acid, you name it), this non-atmospheric part does not have to be comfortable and dry.
It's also dubious (and this is not covered at all by any rule as to water or lava qualify as objects and would be stopped by the dome even on the ground floor. In any case, lava would probably melt the floor around the bubble even if set on the ground, and even though the hemisphere would stay comfortable, you would experience a really nice barbeque effect from touching the floor... ")
b) If it was significantly cold outside, the lack of floor-as-insulation would mean the area inside would not be persistently comfortable as it would lose its temperature equilibrium.
Magic, clearly described.
That being said, for unusual castings, it's obviously up to the DM to rule if the conditions are too extreme, see also "atmosphere" above.
This is straight-forward deal. It must have a floor
Prove it.
and it is therefore a stupendously powerful spell that can’t be Rock-Paper-Scissors interpreted in the kind of ways certain GMs want to in order to block a Long Rest.
Any DM can make any ruling they want anyway.
But this is 5e and you’re the GM! Do like the kid in Matrix (“there is no floor”), tell the rules to go eff themselves, and you won’t have to deal with the problem for your metaplot or for your players deploying this to recharge and screw up your prepped difficulty model because of their resource recharge control!
Honestly, it matters little at our tables, the spell is barely used and certainly not overused, but the description is clear, although after that you can invent lots of things.