The Fadal VMC 4020 uses stabdard Cat CT40 taper tooling, BT40 taper tooling is not compatible with the tool changer, all CT40 Toolholders should have the standard Fadal retention knob (use Loctite) attached tightly onto the small end.
As for tapping your machine should come equipped with the rigid-tapping feature, it works great. If it does not try using a standard CT40 taper, floating tap holder and tapping collets, I wouldn't recommend using a self reversing Tap-matic tapping attachment.
As for broaching, theoritically it is possible using spindle orientation but the machine is not really designed to broach in the traditional sense, you could possibly exceed the machines Z-axis thrust capabilities. I would use a press for broaching.