William Shakespeare is one of the world's greatest playwrights. He was born in 1564 and died in 1616, and during his life he wrote many comedies and tragedies, 38 of which survive today.
Shakespeare's most famous plays include Hamlet, Romeo and Juliet and A Midsummer Night's Dream, and many of his sayings are still in common use today. So if you talk about the mind's eye, good riddance, eating someone out of house and home or something vanishing into thin air, you're quoting Shakespeare.
Elizabeth Arden is an expensive range of women's cosmetics. It was started in the 1960s by a Canadian businesswoman, Florence Nightingale Graham, who quickly became one of the richest women in the world. Mrs Wormwood certainly doesn't hold back on treating herself if this is what she uses.
Rather than the pop star, "madonna" in this context refers to the Virgin Mary, the mother of Jesus Christ and the most painted woman in history.