If Vi attacks a bf with an Overzealous Fan, does the Overzealous Fan ability resolve first so that Vi's ability then fizzles because she is no longer at battlefield?

Yes — Overzealous Fan's ability resolves first, and Vi's ability will fizzle.

Here's the full sequence:

1. Vi moves to the battlefield where Overzealous Fan is. The battlefield becomes Contested. Vi gains the Attacker designation, Overzealous Fan gains the Defender designation.
2. Both "When I attack" (Vi) and "When I defend" (Overzealous Fan) trigger simultaneously. On the Initial Chain, they're placed in order: Attacker first, then Defender (Combat reference, Rule 459). So Vi's trigger goes on the chain first, then Overzealous Fan's goes on top.
3. Overzealous Fan's controller decides whether to use the ability. If yes, they kill the Fan upfront as a cost to place the ability on the chain (FAQ #8702, #9611).
4. Since items resolve last-in-first-out, Overzealous Fan's ability resolves first — moving Vi to her base.
5. Vi's trigger then tries to resolve. Her ability says "[Stun] an enemy unit here." Since Vi was moved to base, she is no longer at the battlefield, and the "here" location requirement fails — the ability does nothing (FAQ #10627, applying Rule 359.3.f.4).

Bottom line: the Fan's kill-and-move resolves first by chain order, Vi is gone before her stun trigger resolves, and the stun whiffs.