Fast as a Kentish oyster i.e. hermetically sealed. Kentish oysters are proverbially good, and all good oysters are fast-closed.
No more sense than an oyster. This is French: “Ilraisonne raisonne comme une huitre.” Oysters have a mouth, but no head.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894