Does this placement of 已經 alter the meaning?
I think the rule is not correct. It should be fine to say


  我沒來上課三天了。


Comparing to 我三天沒來上課了。, the meaning is same but the former puts more emphasis on the duration, i.e. 三天.

Then about the last 2 sentences, 已经 doesn't change the meaning; it's used for emphasizing the duration further.