Being a nidche, everything is mutar as soon as the fast ends – besides for eating meat and drinking wine, which continues until the next morning. This is stated in Halacha.
The reason for this (as I understand it) is that normally the prohibitions continue to midday of the 10th because the Beis Hamikdash continued burning until then. Being a nidche, midday of the 10th has already passed, therefore the prohibitions dont apply any longer. However the prohibition of eating meat and drinking wine is to do with the day of aveilus and therefore the eve folowing the aveilus has the same status as the day.
I hope this is clear enough.