I have no more quests avalible for me in Krokotopia. (Except the vault of ice*.) I just finished the Grand Arena.
*I do have the quest where you have to collect the obelisk rubbings.
Question # 2
Do you have to complete the vault of ice to complete Krokotopia and to get the master of the Oasis badge?
Yes, the Vault of Ice main quest (Breaking the Vault/Find the Fang) has to be finished to complete Kroktopia (along with completing the Tomb of Storms).
You have to do the Vault of Ice. At that point, you'll be sent to the Tomb of Storms. After finishing that (and it's about as long as either the Pyramid or the Krokosphinx), you'll be finished with the storyline quests in Krokotopia.
