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Design question: should the query API validate the argument or just query by the parameter despite whether it is valid?

I think this is partly a matter of taste, but also depends on the use case. In general I'd suggest being strict and validating arguments. This can really help consumers of your api to find errors in their implementation and can in some cases even prevent errors deeper down in your own application flow.
But - as almost always - there are valid reasons for just ignoring invalid arguments or handling them without errors. For example some API providers don't actually want consumers to know which filter options are available. For some technologies this validation would mean much additional effort that might not be worth the investment.