Use of EXP Expedite Descent button is prohibited by most operators due to the automatics inability to control the speed properly. This was quite an old bus, so probably had it fitted, but I'd be surprised if Germanwings allowed its use.
It's not really needed, as you can achieve a safe 5000fpm simply with open descent and very careful use of speedbrake. All this talk of 3500 fom being a hi speed dive is nonsense, certainly a smartish descent but the vs amber caution only come on around 5000fpm. Sorry can't remember the exact figure.
And no, the speed brakes do not automatically deploy, the aircraft protects itself from over speed with a gentle pitch up to recover the normal sped range.