Short answers, pulled from the story.
Sofonisba Anguissola was an Italian Renaissance painter born in Cremona around 1532. She became one of the first and most successful female court painters in Europe, serving Philip II of Spain for fourteen years. Her success opened the door for larger numbers of women to pursue serious careers as artists, and she directly inspired painters including Lavinia Fontana and Artemisia Gentileschi.
In 1554, Anguissola was introduced to Michelangelo in Rome. He challenged her to draw a weeping boy, and she responded with Child Bitten by a Lobster, which impressed him immediately. For at least two years he sent her sketches from his notebooks and offered guidance on her responses, functioning as an informal mentor.
Anguissola arrived at the Spanish court in the winter of 1559-1560, holding the position of lady-in-waiting and art tutor to Queen Elisabeth of Valois. She remained for fourteen years, painting official portraits of the royal family including Philip II himself, his sister Joanna, and his son Don Carlos. She also guided the artistic development of the Queen and later painted Philip's fourth wife, Anne of Austria.
The Game of Chess, painted in 1555 and held at the National Museum in Poznan, is her most famous work. It depicts her sisters Lucia, Minerva, and Europa around a chessboard in an intimate domestic scene that combined formal clothing with candid facial expressions, a departure from the formal conventions of Italian portraiture at the time.
Van Dyck visited Anguissola in Palermo on the 12th of July 1629, recording the encounter in his Italian sketchbook and making a portrait of her. He noted she was 96 years old, with weakened eyesight but clear memory and intellect. He later said their conversation on painting taught him more about the true principles of the art than anything else in his life.
Approximately fifty works are attributed to Anguissola. They can be seen at institutions including the Museo del Prado in Madrid, the Kunsthistorisches Museum in Vienna, the National Museum in Poznan, the Uffizi Gallery in Florence, and the National Museum of Capodimonte in Naples, among others.