You appear to have multiple issues.
First, if your AppleCare plan has expired, all non-warranty repairs will be chargeable at Apple’s standard repair rates.
For qualifying devices, in lieu of a repair to your iPad, Apple will often exchange an iPad for a reconditioned device of the same model and specification - the cost typically being c.60% of the “as new” price of the iPad. As such, in “repairing” the screen, the battery issue will also be addressed.
You can verify eligibility and cost for your country/region here:
iPad Repair & Service - Apple Support