In order to get past the ancient cave paintings in Pokémon Diamond, you'll need to go deal with Team Galatic's HQ in Veilstone. Once you've cleared the HQ the ancient cave paintings should be gone and you'll be able to progress further.
Those are nothing, but they look suspiciously like Mesperit, Uxie, and Azelf.
wayward cave
I think you go to snowpoint and talk to someone and she gives you something to open it.
You can get the TM28 (Dig) on Route 214 in the Ruin Maniac Cave in Pokemon Diamond.
"you" cant
Those are nothing, but they look suspiciously like Mesperit, Uxie, and Azelf.
turn back cave
In Altamira cave, Cantabria, Spain
You cannot find the Pokemon Darkrai in Turnback Cave in the game Pokemon Diamond. Instead you can find him in Newmoon Island.
I beat the league on Pokemon Diamond version, and there was no cave involved, if that's what you were asking.
She is in wayward cave.
wayward cave
I think you go to snowpoint and talk to someone and she gives you something to open it.
You can get the TM28 (Dig) on Route 214 in the Ruin Maniac Cave in Pokemon Diamond.
You can't catch a Lugia anywhere in Pokemon Diamond.
(Apex) Communication.
Early forms of communication