Aston are in because Lawrence Stroll bought the Force India team (which is a long standing team that has raced under many names, originally Jordan, with the iconic yellow snake livery from the 90s) a year or so ago, I think Stroll also bought Aston Martin with the intention of revitalizing the brand or something to that effect and for this year the team now races under the Aston Martin brand, with the goal of challenging the big boys.
That's pretty normal way of F1, many of the teams have existed for decades but race under new ownership/management. The Mercedes team was originally the Honda team after they bailed at the end of 2008 (after having already finished designing the 2009 car), Ross Brawn (team boss) bought the team after Honda bailed and took the finished car into 2009 where they won the championship, then Mercedes bought the team for 2010 (and turned it into the championship monster we have today). But prior to Honda it was BAR, and before that Tyrrell (which goes back to the 1950s).
Drive to Survive is really good, but it's very overdramatized in an American kinda way with a fair bit of creative licence in terms of blowing stuff out of proportion.