How does it work if my opponent moves up to my battlefield and I have an Overzealous Fan at the battlefield? Does my opponent have focus first or me?

When your opponent moves a unit to a battlefield you occupy, a Showdown begins. According to Rule 345, the player who applies the "Contested" status—in this case, your opponent who moved their unit into your battlefield—gains Focus first.

Key points for your situation:

• Opponent has Focus: Because your opponent initiated the showdown, they have Focus and start with the ability to perform discretionary actions (like playing an [ACTION] spell).
• Your Reaction: Even though your opponent has Focus, you are permitted to play [REACTION] cards at any time to respond to their actions.
• Overzealous Fan: Since Overzealous Fan is already at the battlefield when the showdown begins, it gains the "Defender" designation. Its ability, "When I defend, you may kill me to move an attacking unit to its base," will trigger and be placed on the chain. Because this is a triggered ability, you do not need Focus to have it trigger; it happens automatically as part of the game state when the combat begins.

In short, your opponent has Focus to start, but your Overzealous Fan will trigger as soon as the showdown starts, giving you a powerful reactive tool to deal with their attack.