About how many revolutions has the Earth made around the sun?
Since the very early solar system, there have not been large-scale movements of the planets.  

In the early solar system, while the planets were still embedded in a protoplanetary disk, there were large movements. (notably the hypothesised "Grand Tack" of Jupiter) However once Jupiter reached it's current position of 5.2AU it remained there, and the Earth formed then too. 

There have not been any significant changes to the Earth's orbit since the Earth formed, otherwise there would have been significant heating or cooling. So the average year length was and is about 30 000 000 seconds, and Earth has made about 4.5 billion orbits of the sun since then.