Sacking a pilot for allowing a passenger onto a flightdeck seems a little harsh. It does beg the question as to whether it may have been the final straw - or a convenient excuse to offload a "problem".
Pure speculation - but it smells that way to me.
As for using gear to increase the descent rate - very handy trick in a VC10 when spat out of the airway at Kenet (just south of BZN) at FL14 and in need of a steep descent. It's more comfortable than using the speedbrakes (less buffet).
If memory serves, it's 254 KIAS max for lowering but Vmo/Mmo when down and locked.