Ryba is singular. Literally, word for word, it can only be what you said but a valid translation would be Fish and cookies. I don't know the technical English name but the plural fish here are not strictly conveying there are multiple fish, but the concept of fish - we don't know how many. If someone told me they are bringing me fish and cookies I would not expect there to be at least two fish.
I've heard that concept referred to as "uncountable nouns", but I'm not sure if that's the technical name or not.
I like to think of this kind of noun as referring to a substance or material. For example, "Can I have some fish?" or "I want to buy one pound of fish." (This gives the amount of the fish substance, not the number of fishes.)
More examples: "The table is made of wood."; "How much milk is in the bottle?"; "There is some paper on the table."; "Would you like a glass of water?".
What you are talking about are often called 'mass nouns'. The more usual nouns that refer to distinct individual objects are called 'count nouns' or 'common nouns'. And there are also 'proper nouns', i.e. names of specific individuals. As you say there are various phrases where a mass noun is converted into a count noun: 'pound of fish', 'drop of water' etc.