After drawing an epidemic card and infecting the bottom card, do you still need to then infect the number of cities according to the infection rate? Or do you skip the "infect cities" step?
Yes, you must do the infect cities step every turn (unless an event is played to skip it).
From the rulebook:
Each player turn is divided into 3 parts:
- Do 4 actions.
- Draw 2 Player cards.
- Infect cities.
Note that when talking about the case of both player cards being epidemic cards, the rules specifically state that infect cities happens as normal:
In this case in the second epidemic’s Infection card will be the only card to “reshuffle”, ending on top of the Infection Deck. An outbreak will then occur in this city during Infections (see Infections, below)