The repeating key issue could be due to just dirt & crumbs getting stuck in the Butterfly keyboard mechanism (design & manufacturing defect). However, since your Battery is saying "Service Recommended", then you should only mention the bad Battery since the Top Case Keyboard Assembly will also be replaced during the repair since the Battery is glued to the underside of the Palmrest & Trackpad. The Trackpad, Touchbar & Speakers are also part of the Top Case Assembly so they will also be replaced when the Battery is replaced. If you mention the bad key & the tech focuses on that, then the tech may quote you for the full price of the Top Case Assembly instead of the Battery only price for the same exact part.
As for the price, you will need to have Apple or an Apple Authorized Service Provider examine the laptop to provide you with a repair estimate since the price may depend on how the laptop is repaired and your region. Here is an Apple page with some repair prices listed....it shows $249 US, but make sure to confirm the price with the AASP.
Mac Repair & Service - Apple Support
FYI, here is an Apple article with instructions for cleaning the laptop's keyboard....just make sure to keep the can of compressed air completely upright or you will damage the laptop with the cold wet propellant.
How to clean the keyboard of your MacBook or MacBook Pro - Apple Support
