Do you think Vriska would be able to make the beta kids, the alpha kids, Kanaya and Karkat fall asleep, one after the other? (assuming she's still maintaining her mind control on all of them)

Betas and Alphas, yes. Kanaya and Karkat, though, not quite. She can only make Humans fall asleep because of weird biological differences- I believe she cannot control Kanaya? Not quite sure about Karkat.