Hi,
a) a sell-by date I'm not familiar with this. I guess it would be a date marked on a product, after which the store should take it off the shelf and no longer sell it.
b) the / a (?) best-by date The date marked on a product to indicate when it will be past its best condition. eg on a milk carton,I suppose. It can still be sold.
c) the / an expiry date This is the date when something becomes invalid, no good. My passport has an expiry date, after which I need to get a new one.
Are "sell-by / best-by / expiry" kind of adjectives? Yes.
You can use 'a' or 'the', depending on whether you want to be specific or not.
Every product on the shelf had a best-by date.
The best-by date on this carton of milk is tomorrow.
Best wishes, Clive