A) A new roe kid in the last week of March is quite possible, though very early as you will appreciate. The peak of fawning in the south of England is mid-May, though older females tend to produce up to a week earlier than does having their first young. The earliest date in my experience was 30 April and was a desperately sad sight, as a difficult presentation of the foetus had made for a prolonged labour, during which the mother had died without delivering her kid.
As this kid was apparently pretty agile, it sounds as though it was more than just newborn, which makes it all the more unusual. I have, however, reliable records of live roe kids as early as the first week of March and these, surprisingly, from Scotland. Warm weather may accelerate the growth of the foetus to produce an earlier date for delivery and this may vary according to a late winter and spring weather. However, no-one could say that this past winter was unusually mild. Such an early kid also brings into question the extension of the doe season to include March, an extension which, I believe, has been a grave error.