The show made a fair few changes from the books, mostly for the better. Off the top of my head, Avasarala and Draper are introduced earlier in the show, Drummer got the consolidated stories of several other side characters and Elvi Okoye’s and Ashford’s personalities were significantly changed. IMO, Show Ashford is a much more interesting character than Book Ashford. In addition, the season 6 side plot with the kids is told much later in the books.
Because if you launch something from Earth, you inherit the Earth’s orbital speed around the Sun. At that point, whatever you launched will just continue to orbit the Sun. It takes less energy to accelerate to a solar system exit trajectory than it does to scrub off all of the excess velocity and end up on a trajectory that intersects the Sun.