Just a couple of points on this subject:-
1) Concorde like all other aircraft has to proove it can descend to a safe altitude (14,000 ft if I remember correctly ) in the required time.
2) From supersonic it's rates are not that great initially as it first has to partly slow down before it descends. Once below 30,000ft and below a certain speed, it can use it's two inboard reversers in reverse idle thrust, and then the rate of descents can become quite high ie somewhat greater than 10,000ft /min, but 34,000ft/min he must have been kidding you. Oh yes the altimeter is calibrated at least up to 10,000 ft/min
3) Concorde flight crew have all got "Pressure Breathing" at their individual stations, which is supplied via a quick donning mask. Every so often (two year intervals ? ) the crew have to
practise donning the mask in the required time and using the pressure breathing, albeit at a reduced pressure to what they would get in flight. This is monitored by a Doctor as the proceedure is somewhat dangerous. Makes you go red and puts your blood pressure up. No other type of civilian aircraft has this system, but they do have 100% oxygen systems
Regards
