Like Vid said, there's a flipper enable relay on the solenoid driver board. It should pull in during gameplay to give the flipper coils a path to the cab switches. A locked on flipper relay would explain the flippers being active in attract mode.
J1 and J2 are where the flippers coils and cab switches connect to the driver board. Any intermittent connections here would cause intermittent flipper behavior. It's always a good idea to rebuild these as they're quite prone to failure. Also check to make sure left cab switch and EOS are clean and properly adjusted.
The phantom sling fires could be a number of things. First check to make sure the sling switch contacts aren't gapped too close. If they're good, try clipping one leg of the ceramic disc capacitor wired across the sling switch. If the phantom closures go away, replace the cap.