If it is my turn and I control a battlefield and move my Irresistible Faefolk from base into that battlefield using its effect to move a Vi Peacekeeper into that same battlefield, will the Vi Peacekeeper get to stun with its effect and why?

Yes, the Vi, Peacekeeper will be able to use her ability to [Stun] an enemy unit.

Explanation

When you use Irresistible Faefolk to move an enemy Vi, Peacekeeper into a battlefield you control, a Combat Showdown begins because units from opposing players are now present at the same battlefield.

According to RiftJudge FAQ #10034, #10437, and #10581, the key to this interaction is that when Vi, Peacekeeper enters the battlefield during an ongoing showdown, she joins the combat. Here is the step-by-step sequence:

1. Trigger: You move Irresistible Faefolk to your battlefield. Her ability triggers, allowing you to move an enemy unit (Vi) to that same battlefield.
2. Combat Initialization: The arrival of the enemy unit triggers a combat showdown.
3. Designation: Because your opponent now has a unit present in a battlefield you control, they become the Attacker (per RiftJudge FAQ #7385 and #9843).
4. Vi Joins Combat: When Vi, Peacekeeper enters the battlefield (or is moved there by your effect), she joins the ongoing combat. Upon joining, she is designated as an Attacker.
5. Trigger: Gaining the "Attacker" designation fulfills Vi’s "When I attack" trigger condition.
6. Resolution: Her ability is placed on the chain. As long as Vi, Peacekeeper remains at that battlefield ("here") when the ability resolves, you may choose an enemy unit at that battlefield—which could be your own unit—to [Stun].

Important Considerations

• "Here" Constraint: As per RiftJudge FAQ #10045, Vi, Peacekeeper must remain at the battlefield when her ability resolves. If she is removed from the battlefield (e.g., by another effect played in response) before her ability resolves, her ability will fail to find its source and will not [Stun] any unit.
• Stunned Status: Per Rule 423.1.a.1, a unit that is already stunned cannot be stunned again. If you choose a unit that is already stunned, the effect will fail to trigger any further "when you stun" effects (if applicable).
• Timing: Her ability triggers exactly once when she gains the Attacker designation upon entry.

This is my interpretation based on the standard rules for combat designation and triggered abilities. No official FAQ exists for the specific interaction of moving an enemy Vi, Peacekeeper into a battlefield using Irresistible Faefolk, but it follows the established rulings regarding how units joining a showdown function as attackers.