In North America, the verb "to hash" has the primary meaning of to cut or chop meat or vegetables into very small pieces, but "to dice" is a more common synonym. Just as "chopped vegetables" uses the past participle "chopped" as an adjective, "hashed potatoes" uses "hashed" as an adjective. Hashed pototoes, hashed browned pototoes, and hash browns are equivalent American and Canadian names for small pieces of pototoes which are fried ("browned") and eaten as a breakfast food. Corned beef hash is another breakfast food made of small pieces of beef and potatoes. New Oxford American Dictionary hash | hæʃ | noun a dish of cooked meat cut into small pieces and cooked again, usually with potatoes. verb [with object] make (meat or other food) into a hash. • North American chop (meat or vegetables). hash browns | ˌhæʃ ˈbraʊnz | (also hashed browns) plural noun chiefly North American a dish of cooked potatoes, typically with onions added, that have been chopped into small pieces and fried until brown.

If they said '"Hashed Potatoes", I wonder if it wasn't either comedy or poor English. Also, 'hashed potatoes' is probably butchered English, something I would never expect a native speaker to say. "Hash" or "Hashed Browns" are two different things, but both understood by native speakers.

Literally, it means "potatoes made into a hash." In this case, it is probably someone's cutesy way of saying "hash browns."

Not certain.

I see, perhaps it is a specialty in this restaurant hhh.