Name of anime where the winner of a competition would inherit the forest
I know this anime. It's Baby Baachan.



The main girl is Amika, who fights to save the forest which her grandmother has protected. The other girls are other granddaughters of the grandmother. The grandmother possesses her baby brother's body and tries to teach Amika how to win. She hates it till the end. The rounds go exactly as you say. In between, the grandmother/baby offers useful tips like cutting onions without crying, etc.

I will never forget this anime because the tips in this series helped me a lot in life when I was young. Hope this helped :D