IMHO the ending was kidna stupid. Xerxes being killed would mean the execution of both of the girls via his guards. Terrible ending via the circumstances.
Not necessarily. It would depend upon the prevailing traditions, but if a king died without heirs, in most kingdoms (classical, medieval and even in more modern times) they wouldn't allow a commoner to accede to the throne because that would destroy the entire mystique of kingship. Instead they would invite some other person of royal blood (a prince or princess from a neighbouring kingdom) to do so, as the English did in 1689 and again in 1714. The person they would invite, in all likelihood, would be Larisa.
Even if Xerxes did have heirs, his death would in all probability be interpreted as a divine judgement upon him and all his progeny – especially if he'd been feared and loathed in his lifetime. In that case, again, they would in all probability offer the throne to Larisa, who, let's face it, has all the attributes one could ever wish for in a monarch.
The most interesting question is this: what if Xerxes had one heir and one heir alone: a proud and beautiful daughter the same age as Larisa? Those seeking continuity (few in number, I expect, if Xerxes was the tyrant one imagines) would champion her cause; those seeking regime change would champion that of Larisa. Call me a snowflake, but the only sane way I can envisage of resolving the conflict in that case would be to send them alone into the arena before the eyes of the entire nation and let the gods decide. If the princess less favoured by the gods was not killed outright in the course of the duel, she could always renounce her claim to the throne by prostrating herself before her conqueror and laying the crown at her feet.