The resonator duct is between the MAF and throttle body, so it was causing the MAF to under report air, resulting in less fuel being injected, mixture problems, misfires, and likely the cat efficiency codes. The failed DISA valve is for torque boost and has no effect on misfires but it could could create a vacuum leak if it leaks where it attaches to the intake. If you don't want to replace it you could remove the loose/broken parts and reinstall.