I've told you repeatedly I don't judge my players or evaluate their skill in any way that affects the game. Occasionally I'll discuss lack of tactics with my wife outside of the game but it has zero impact on the game itself.What are the amounts? How do they know them? How can the players act on them?
Players, not PCs. How do these things come to the players attention? In what format? Narration of events by the GM? More than that?
Even if they know these odds, what does that matter if the GM is free to just decide how it all turns out?
You hadn't answered yet.
I'll tell the people make a dex save for half, most of the time I'll tell them the DC if it affects multiple people. I won't tell them that it's the legendary action of an adult red dragon in it's lair.So a couple things on this. Clearly, they know there is something causing a magma geyser... I'm guessing the scene was in a volcanic type location, or the enemy was some kind of fire themed monster. If so, they're likely to grasp "this is a property of the environment/monster" even if they don't know exactly how it works (i.e. determined randomly in some manner, or GM decides who gets hit and when). That they will need to make a saving throw is also understood, likely for half damage? (Uncertain, but that's pretty typically for area attacks like that).
I don't care if you don't see what it adds.They likely also know that they may be able to use applicable skills to learn more. They understand that these are the processes of play, and what goes into them. It's all part of a combat encounter, which has as much structure to it as 5E offers.
Now, I'd question what withholding any of that really adds to play. Like if you want there to be uncertainty on the part of the players.... like "I'm worried when one of those magma geysers will hit" you can actually replicate that with the uncertainty of a dice roll. Uncertainty doesn't have to come from withholding information from the players.

I follow the rules of the game. The rules state how a nature or arcana check can be used but are silent on what kind of action it would require in combat. I now use XGtE guidance for identifying a spell, it's a reaction. Some checks are free others take an action.My second thought on this is what if you just discarded some of the structures that are involved? Like, they don't get a save, they just are hit by magma and take 20 damage. No, they can't use Nature or Arcana or Investigation checks to learn any more. And so on. Removing the structure would likely have a negative impact on the play of the game.
You've never played at my table. You don't get to tell me whether how I DM has a negative impact on the game, especially when it comes to rulings on how things work.