Answer to Question 1
The extremely dense material could not be supported by the ordinary material on Earth and it would plunge to the center of Earth under the action of gravity. Its momentum would carry it past the center, back to the other side and it would continue to oscillate back and forth through Earth creating a small hole each time (that would rapidly fill with molten rock) until friction finally brought it to rest at the center of Earth.
Answer to Question 2
TRUE