The amount the ride would have moved it about would be phenomenal it could be miles away. I wouldn't waste my time as its probably trashed anyway.
Highly unlikely, gold is a dense, heavy metal, it won't have gone that far even with longshore drift, except over a fair period of time. It probably won't have moved more than a few tens of meters, if that. Certainly worth going and spending an afternoon with a detector, provided you know exactly the spot on the beach where you lost it.
And how could a solid gold ring get trashed in wet sand? It's not like it's getting run over by a train, or smashed with a hammer!