I did straight sets most of the time but Eric also likes something he calls the "Rule of 90%". For example, you ramp up on your warm-ups for front squat something like 95x5, 135x4, 185x3, and then 225x6 is a near max, within one rep of failure set.
That was your first set of 6 and today calls for 4x6 so you have 3 more to go. The weight on your next three sets should be within 90% of your top set. So 220x6, 210x6 and 205x6 would all count but 195x6 would not. Ramping up to a top weight on your first set and then gauging the others off of that is a sound strategy. If you do the same exercise two sessions in a row than that helps too since you already have a frame of reference.
You could also warm up the way you posted (165x4, 175x4,185x4,195x4,205x4), in that case your 185x4, 195x4 and 205x4 sets would all count towards your 5x4 for the day. You would need two more sets in between 185 and 205 to finish up.
As for box squats I would encourage you to do them as long as you're doing them properly, Westside style. By that I mean a controlled negative onto the box, no dropping, a slight rock on the box and then hip and leg drive off of the box with no good morning-ing. Box height should be around parallel with for most people of average height is not a bench. I did actually use a bench for most of the program and gained 50 lbs on my free squat but my sticking point is in the quarter squat position which is very unusual.