Should a Muslim woman demand from her apostate ex-husband alimony for their daughter, and a division of the commercial workshop he had gifted to her when he was a Muslim, and is she entitled to divorce maintenance?

The mother has the right to custody of her daughter and to demand from the father her maintenance and necessities until she marries. However, there is no obligation for the divorced mother's maintenance during the waiting period (iddah) due to the dissolution of the marriage by apostasy. She has the right to demand what the father gifted her if she took possession of it, because a gift becomes ownership upon acceptance.