In BE we would use "Did you ever see" when asking about something someone might have done during a completed period in the past.
Iain: When I was young I used to go fishing in Loch Ness.
Mary: Did you ever see the Loch Ness Monster?
(he does not go fishing there now, so she uses the past simple)

In BE we use "Have you ever seen" to ask about events during a person's (unfinished) lifetime.
Mary: Iain, have you ever seen the Loch Ness Monster? (=in all your life)

In AE people also use "Did you ever see" for this, too:
Sue-Ellen: Jim-Bob, did you ever see the Statue of Liberty? (= in all your life)
(Disclaimer: I'm not American.)

Fine, thank you.