Which club won fa cup and was still relegated?

Answer 1

In total 6 teams have reached cup finals and got relegated, none of them won the cup though.

1. Chelsea ( 1915 )
2. Manchester City ( 1926 )
3. Leicester City ( 1969 )
4. Brighton ( 1983 )
5. Middlesbrough ( 1997 )
6. Portsmouth ( 2010 )

Answer 2

Yes. Norwich beat Sunderland in 1985 - both teams ended up going down that year.

Answer 3

I'm not sure about the FA cup, but Birmingham won the Carling Cup in 2010-11 and still went down.