another rasam is that the new bride reads a couple pages of quran and then gives some small amount of money in sadka. this is right after entering the new home.
Yes, the dulhan cooks kheer usually that traditionally signals that she will begin housework now. There is also in some families deaseera ki rasm usually in bihari families where the new bride and groom go stay at the girl’s parents’ house for a few days. It used to be ten days but now its not a hard and fast rule.