"I see your team's in the final. HAVE they ever WON the cup?" is correct!

The first sentence tells you which form to use. :) "I see your team's in the final." = talking about the present. "Have they ever won the cup?" = talking about the present. If you're talking about the past, it will go something like this: "As part of my sporting career, I managed a football team for about fifteen years." "Did they ever win the cup?" (ie. in the past, when the first speaker was manager.)

Actually you can use either. "Have you ever" and "did you ever" are roughly the same expression.

Technically, using the past perfect is correct. "Have they ever won the cup?" But it is common to use the simple past to express the same thought when you are talking about a specific event.