"Do I like the duck?"
Translation:Mag ich die Ente?
"Die Ente mag ich" is equal to "Ich mag die Ente" - in both cases the verb is the second word in the sentence. If you use it as a question, it is like you say "I like the duck?" instead of "Do I like the duck?" in English. Verb should take first place in a sentence that's a question in German: "Mag ich die Ente?". Hope my English is good enough to understand me.
"Gefallen" and "mögen" are used quite differently. "Mögen" means "to like" and is used the same way, with an accusative object: "Ich mag die Ente" = "I like the duck." "Gefallen" essentially shows being liked (roughly "to please"), and, as you have in your sentence, the subject is liked by the dative object: "Die Ente gefällt mir" = "I like the duck." So "Mag mir die Ente?" is simply ungrammatical; it should be "Mag ich die Ente?" with the subject "ich."