Should I take protein shakes on days that I don't work out?
Yes that's right muscle growth
takes place when you rest not when you workout, so protein when you
rest is just as important as on the day you workout, personally i have 3
protein shakes a day, 2 of those are 1 scoop and my post workout is 2 scoops so 4 servings total, and on the days off i have 3 single servings spread throughout the day.
You've got it right with the 2 scoops after a workout though as its
important to take advantage of that window when your muscles are drained
and a big 40g serving of protein is ideal.