In my opinion:
A) Yes- they give the specific example of (e.g. the 7 in F7A2-EM12K)
B) I do not believe so. If they meant classification, I think they would have stated it that way. This is a non-essential variable, so changing "designation" would not require requalification. I think they are talking about a manufacturers designation.
C) I think they are talking about the whole electrode/flux classification here. Again, it is non-essentail. So for example, changing from F7A2-EM12K to F7A4-EM11K would not require qualification based on this variable.
D) Although changing to a lower temperature classification makes sense to not have to re-qualify, it does not give that exemption, so it looks to me like requalification is required for any change in the AWS class except for hydrogen, when supplemental essential variables apply.