4. g would steadily decrease as the center of the earth was approached, until g is exactly zero at the center.
5. At the center of the earth, the actual velocity will still be faster than the calculated terminal velocity due to momentum. g is now zero, so the penny's weight is zero (but mass doesn't change). Air pressure and therefore drag are now at their maximum.
6. The penny would continue traveling past the center of the earth due to momentum, until the air resistance and gravitational force from the opposite side stopped it. Gravity would then pull it back toward the center of the Earth, and momentum would bring it back toward the side of the Earth that it started from.
7. It would oscillate back and forth thousands of times, in ever decreasing movements due to the friction of air resistance, each time centered on the center of the earth. Every time the penny passes through the center of the Earth, it would be traveling a bit slower. The oscillations are a "yo-yo" or "pendulum" effect known as simple harmonic motion continuously dampened by friction from the air.
8. Air resistance would dampen the up and down (relative to the departure point) oscillations until a steady and perpetual state of no movement was reached exactly at the center of the earth in a state of weightlessness and gravitational equilibrium. There is no gravity at the center of the Earth because there are equal amounts of mass surrounding the penny.
Assuming of course there was no molten rock in the hole!
This is a commonly asked question which leads to a good study of the interaction between the various physical forces and principles - motion, momentum, gravity, drag, mass, density, acceleration, and velocity - and the laws that apply to them including all three of Newton's three laws of motion.