If X is 0, you’ll perform the process just once when Another Round resolves.

You don’t have to choose the same set of creatures each time you repeat this process.

Once an exiled creature returns, it’s considered a new object with no relation to the object that it was. Auras attached to the exiled creature will be put into their owners’ graveyards. Equipment attached to the exiled creature will become unattached and remain on the battlefield. Any counters on the exiled creature will cease to exist.

If a token is exiled this way, it will cease to exist and won’t return to the battlefield.

Abilities that trigger “When [this creature] enters the battlefield” or “When [this creature] leaves the battlefield” will trigger each time that creature enters or leaves the battlefield as a result of Another Round’s effect. If those abilities require targets, you won’t choose those targets until after Another Round finishes resolving, when those abilities are put onto the stack.

All abilities that trigger while Another Round is resolving are put on the stack after Another Round is finished resolving. All such abilities controlled by the player whose turn it is are put on the stack first, then those controlled by the next player in turn order, and so on. For each player, they can put their abilities on the stack in the order of their choice. Abilities don’t have to be put on the stack in the order in which they triggered.