In general, if Dress Down is already on the battlefield, Walking Ballista will enter with no +1/+1 counters on it (regardless of the value of X). The same is true for a creature with modular (C.R. 702.43a). (As a result, if the creature's toughness is 0 or less, it will go to the graveyard as a state-based action [C.R. 704.5f].)
Both cases involve replacement effects that modify how the creature enters the battlefield, but "[t]o determine which replacement effects apply", the game "check[s] the characteristics of the [creature] as it would exist on the battlefield, taking into account ... continuous effects that already exist and would apply to the permanent", among other things, and that includes the effect of Dress Down (C.R. 614.12). Thus, since the creature would be seen as having no abilities due to Dress Down, those abilities' replacement effects don't apply, so they won't give any counters to the creature.