Welcome to Using English.
Yes, the first one should be "every dozen yards." I am trying to think of why "each" doesn't work and all I can think of is that it's just idiomatic and it sounds "right" to a native speaker to say "every." I hope that someone else will come along with a better answer.
The second one should be "the second one" just as you have written. However, there is a tense problem in the question itself: As we have finished. Also, the word order is more natural as "we will now read" instead of "now we will read" but that is just my opinion. The finish/finished is an error.