According to my knowledge the sheet should charge up negative. Since the plastic is not conductive the charge on it cannot wander around. This means that some regions might get charged up more than others and some may recieve no charge at all. The electric field generated by the sheet is therefore most likely nonuniform. This electric field will induce regions of irregular charge distribution on the tray (think of the charge on the tray as being kept there [frozen] by the electric field produced by the sheet).
Question 1: "Will this charge be of the same (negative) or opposite charge as than on the sheet?"
Question 2: "How will this charge on the tray influence the stryrofoam pieces resting on it considering the fact that styrofoam is also nonconductive?"
Question 4: "What effect will the irregular charge distribution on the tray have on the stryrofoam pieces?"
Question 5: "Can the electric field induce an irregular charge distribution on the styrofoam pieces since some parts of the stryrofoam is closer to the sheet than others?"
Question 6: "Under what circumstances do you think that two nonconductive objects can exert electrostatic forces on each other?"