No, the earth is not shrinking and the density of the earth is not changing. Nor is the frequency and size of earthquakes increasing. Though it is pumped out of the earth, all the oil stays here on the planet, even after it burns. When oil is burned it is just being converted to water and carbon dioxide (CO2) and a few other trace chemicals. It all stays here, and does not escape the gravitational pull of the planet. The overall average density of the Earth remains exactly the same. We had a similar question some time ago.
In that question, we point out that the oil comes from porous rock formations. Hence while the oil and gas is pumped out, the rocks remain, so there is no great difference in most cases. Also, please remember, oil is being extracted in relatively very few places around the planet.
On another note, although to us little humans, the amount of oil that is being pumped out seems like a lot, compared to the entire mass of the Earth it is a teensy tiny amount. Even relative to the amount of water on the planet, it's ultra small. To put this in perspective, consider this: the amount of CO2 in the atmosphere is so small it is measured in parts per million. The Mauna Loa record (which is arguably our best measure of increasing carbon dioxide in the atmosphere) shows a 19.4% increase in the mean annual concentration, up from 315.98 parts per million in 1959 to 377.38 ppm in 2004. So think of a sample of air with all its components separated out and filling one million cups. Only 377 of those million cups would be full of carbon dioxide. By far the most, 780,840 cups are nitrogen and 209,460 are oxygen. Even Argon which we think of as rather rare would fill 9,340 cups--30 times more cups than carbon dioxide. And this is AFTER 100 years of mad burning of all the oil to form CO2. The water in the air would fill about 10,000 of those million cups--again 30 times more than the CO2.
A pie graph showing just how tiny the carbon content of the atmosphere is can be found at Wikipedia.
The point is--and it's hard for us humans to believe because we do tend to think of ourselves as being very superior and great--is that the planet is MUCH MUCH bigger than us. Though we are doing a lot, and arguably some of it is very bad, we are small potatoes compared to everything else going on here on Earth.
I would like to add that personally I am still waiting to see if the global warming theory is true, but I strongly believe that the rate of extraction and burning of oil is far too high. Insanely high. I feel we should conserve oil and develop other ways to fuel cars. Burning all the oil is analogous to the way earlier peoples burned all their trees for fuel without thinking. Soon they found they had no trees for houses, tools, or boats and eventually they all died. There are many better things we can do with oil than simply burn it; we can make things with it. I wish environmentalists would stop harping on the global warming issue and start to explain all the marvelous things that can be done with oil. We should conserve it for these precious uses and stop the reckless burning of it.