As far as birth dates go, most parish records of the 18thC won't give that information - they only record the date of baptism. Sometimes, if you consult the original registers, a helpful vicar may have added the birth date scribbled into the margin but this gets rarer the further back you go. You may find birth dates mentioned in other documents (wills, burial registers, poor law documents, marriage licences etc.) but that can mean some digging about in the archive.
Parish records and other documents relating to Burford are available at Oxfordshire Records Office, they are also quite well covered on FamilySearch (it has Maria Smith being christened on 29 Dec 1766 at Burford.) The Oxfordshire records office also has a number of other documents relating to Christopher Kempster in its catalogue.