~ㄴ/은 적이 있다/없다 is a grammatical phrase for saying "have done something/have not done something" (in your life). 보+ㄴ= 본
ㄴ적 is used to express a past experience, so 본적 is having the past experience (적) of seeing (보) something. Like a dragon's fingers, for instance. :-)
This translates to something closer to "have you ever seen the dragons fingers" ~을 본 적 있다/없다 is a form expression having ever or having never done something.
Seems a bit strange to be using the banmal 너는 with the incredibly formal 있습니까. I'm sure it would be more natural to either omit the subject or just use 있어, depending on who you're talking to.
its not actually an unusual combination, as using 저 doesnt raise or lower the listener but makes the speaker sound humble. it can be possible to raise the listener without lowering yourself.
inversely, if your try and lower yourself while speaking down to the listener, well, you will probably just sound sarcastic.
But both 너는 and 있습니까 are dependent on the listener. Why would one use a banmal term for "you" but use a formal verb ending?
embarrassing. i read it as 나. you would probably never see this combination, though duolingo doesn't care about whether the honorifics make sense. it only cares about whether you type it in the one exact specific combination that whoever haphazardly spammed into place.