2.) Do we have a word for "To provoke someone to envy"?
2.) Ana has a chocolate cake. And she's teasing Bea of her cake. How would I put that in a sentence(informal)?
to "make someone jealous" might do.
Mary had a piece of chocolate cake and showed Sue to make her jealous.
You can't make someone have envy. They get that feeling themselves.
Sue was envious after seeing the cake.