Model number of battery -- do not have this, you will need to reach out to an Apple Authorized Service Provider or Apple Retail Store to see if they are able to give this to you.
Mac battery replacement prices are listed here: https://support.apple.com/mac/repair/service
If repair is done through Apple or an Apple Authorized Service Provider, there is typically a 90 day warranty on repairs.
Our guarantee after service:
"We guarantee our service, including replacement parts, for 90 days or the remaining term of your Apple warranty or AppleCare plan coverage, whichever is longer. We offer this whenever you get service from us or from an Apple Authorized Service Provider. This is in addition to rights provided by consumer law."
Read the Apple Repair Terms and Conditions
To schedule an appointment at an Apple Authorized Service Provider or Apple Retail Store: https://getsupport.apple.com > choose hardware issues or you can go to: https://www.apple.com/retail/geniusbar/
If wanting to mail-in, contact Apple support to see if available in your region.