You could say "I fancy he's a friend of yours". But that would sound a little weird here. I would say "I imagine he's a friend of yours".
Yes, if you "fancy somebody" you're sexually/romantically attracted to them. But that usage sounds outdated to me and I would ever use it only jokingly/sarcastically.
You can also "fancy something" if you want it. "I fancy a hard boiled egg for breakfast".
I fancy that British people use fancy like this. At least, I hear it in their shows and not in American ones.
I would ever use fancy only as an adjective.
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