1) The OED links these two spellings with meanings such as 'imitated, forged' or 'made to a pattern, wrought', even 'made of inferior materials' but in Yorkshire some examples suggest that it came to mean a basin, made of some kind of metal.
1433 et unam pelvim vocatam counterfete cum lotorio, York
1486 a counterfete basyn with a lavour of laton, Hull. It was commonly used of pewter items: 1546 all my pewther vessel ... chardgers, dublers ... salte sellers, and Counterfottes, Wakefield
1567 Item two garnishe of vessell in either 12 Dowblers 12 dishes 12 sawcers one great charger 8 podyngers 16 counterfettes ... five saltes, Fixby.