"Nach dem Befinden fragen" isn't a sentence, it's just a verb with it's prepositional object, which might be part of the confusion. A grammatically more correct translation would be "to ask [someone] about state of health", or, more freely, "to ask [someone] how they're feeling". DeepL left out the word "to" that is normally used in English to mark an infinitive, that's why the English translation looks like an imperative.
"To ask about something" is "nach etwas fragen" in German. It's the same grammatical structure, just different prepositions and word orders.
"Das Befinden" is a fancy noun for the state of a person's health or well-being.