(1)b平方-a平方=1/2c平方，
由正弦定理，(sinB)^2-(sinA)^2=(1/2)(sinC)^2,
A=π/4,B=3π/4-C,
∴[(√2/2)cosC+(√2/2)sinC]^2-1/2=(1/2)(sinC)^2,
∴(cosC+sinC)^2-1=(sinC)^2,
∴2sinCcosC-(sinC)^2=0,sinC>0,
∴2cosC=sinC,cosC≠0，
∴tanC=2.
(2)sinC=2/√5，cosC=1/√5，
sinB=(cosC+sinC)/√2=3/√10，
由正弦定理，a=bsinA/sinB,c=bsinC/sinB,
∴S△ABC=(1/2)acsinB
=(1/2)b^2*sinAsinC/sinB
=(b^2/2)*1/√2*2/√5*√10/3
=b^2/3=3,
∴b^2=9,b=3.