The tokens copy exactly what was printed on the original Aura and nothing else (unless that Aura was itself copying something else; see below). It doesn't copy whether that Aura was tapped or untapped, whether it had any counters on it or Auras attached to it, or any non-copy effects that changed its types, color, and so on.

Since Three Dog's reflexive triggered ability doesn't target, Aura tokens created by that ability will be attached to attacking creatures you control with shroud.

Any enters-the-battlefield abilities of the copied Aura will trigger when the tokens enter the battlefield. Any "as [this Aura] enters the battlefield" or "[this Aura] enters the battlefield with" abilities of the Aura will also work.

If one of the Aura tokens being created couldn't legally be attached to the appropriate attacking creature (because of an ability like protection from enchantments), that Aura token won't be created.

If the copied Aura had in its mana cost, X is 0.

If the copied Aura was copying something else, the tokens enter the battlefield as whatever that Aura was copying.