If Karkat and his friends have successfully won their session, why were they help/messing with the kids in the first place? Also, how old exactly are the trolls from Aranea's crew compared to Jane and her friends?

They saw that Bec Noir came from the kids’ session and began trolling them because they thought the kids’ sent him on purpose. Aranea and her group are nine sweeps old which is roughly nineteen and a half years old. Jane and the other kids are all sixteen.