A) It is quite usual for a buck following a doe in full rut to lie down, quite simply because the animal becomes tired. In fact, I have seen a doe literally prodding her consort to get up and keep going. It is the doe who dominates, choosing the place where she ruts and which buck she fancies.
It looks as though you had a rare sight of a hummel roe. Sometimes a buck may just have flat plates of antler on each pedicle but, unlike the red deer, true male roe lacking any antlers are very scarce. Over the past 50 years I have only four confirmed records of one being shot.
As far as suckling is concerned, with regard to roe, there is some variation in birth dates and this could have been a late fawn. The date of weaning tends to be later the further north one goes, but in the South most does will be dry by the end of the rut.