What is this?
That is a Seated Goddess! Unfortunately, we don't know exactly which goddess the sculpture is meant to represent. This particular sculpture was made of plaster and wood. Considering the materials used, it is in remarkable shape! This statue and others in the same case show idealized female bodies in ancient Egypt. The bright blue fragment, for example, shows the goddess Isis. The remainder of the statue would have shown the goddess Isis nursing the god Horus as a child.
What materials and tools were these made with?
The larger figure to the right is made of plaster and was formed in a mold. It would have been painted as well, but much of the paint has come off. You can still see some in her hair.
What was the purpose of these sculptures? Were they important people?
These figures all had some kind of religious significance. Isis, represented in at least two of them, was one of the most important goddesses in the ancient Egyptian pantheon.
The larger limestone figure is also identified as a goddess, but without an inscription, headdress, or other defining attributes, so we can't be sure which one.
The headless figure is also difficult to securely identify, but the scepter she holds suggests that she represents either a queen or a goddess.
Why do they hold their chest?
The headless figure is simply holding her scepter close to her body, a useful feature in sculpture to make sure parts don't break off.
The two busts of Isis would have actually included a representation of her son, the god Horus, as an infant nursing. They are holding their babies to their chests.