Ooh~ 🎶 several of the characters sing and dance!
Let's start with the three characters I mainly write about:
Eula, of course, LOVES to dance. She's incorporated dancing into her fighting style. In the context of Euluc, I do imagine that she gets Diluc to dance, and my headcanon is that he knows how, but hasn't danced in a while so he gets shy about it.
I like to imagine that Diluc and Kaeya did take music lessons as children, where Diluc played the violin and Kaeya played the piano. (I have some fanart I saw somewhere to thank for that.) All of it is for fun, not professional.
If they were asked on the spot to sing, Eula or Kaeya might, depending on who's asking. Alcohol might sway their opinion. I don't feel like Diluc would sing - I think he's more private.
As for Genshin characters I don't write about as often (and OCs):
Furina loves to sing AND dance, which I show in The Chaos War a few times. She would sing or dance on the spot - she's done it more for fun but did it with a troupe before too. She's more of a director now I believe.
Adelinde can sing but she does it more privately. I have a headcanon where she used to sing lullabies to Diluc and Kaeya when they'd have nightmares, to help them fall asleep.
I have the same dynamic for Zorina and Sorin, where she serenades him to sleep when he's anxious. It soothes her nerves and his. I even have a song that matches perfectly for them.
If Adelinde or Zorina were asked to sing, I feel like they would politely decline, smiling behind one hand and changing the subject quickly.
Sorin doesn't sing or dance, and if he was ever asked to, he'd probably decline out of embarrassment and just glare at the person who's asking, like they've offended him 😅