Does the Ezreal Prodigy ability allow me to attach Gear for free? Does attaching the Gear count as an optional cost?

No, Ezreal, Prodigy does not allow you to attach gear for free, and the Equip cost does not count as an optional additional cost.

According to the official rulings and game rules:

1. Equip is an Activated Ability: Rule 744.1 states that "Equip is an Activated Ability keyword." Because it is an activation cost for an ability, it is neither "optional" nor "additional" in the way the game defines those terms for spellcasting.
2. Definition of Optional Additional Costs: Ezreal specifically reduces costs that use both the words "as an additional cost" and "may" (Rule 353.2.b.1). These are typically found on keywords like Repeat and Accelerate, or specific card text like Blast Corps Cadet.
3. Direct Ruling: There is a specific FAQ regarding this interaction:

   "Ezreal, Prodigy reduces additional costs that are optional to pay... Ezreal can’t reduce Equip costs. That’s an activation cost for an ability, so it’s neither optional nor additional."

Summary: You must still pay the full listed cost to use a Gear's Equip ability while Ezreal, Prodigy is on the board.