I'm somewhat startled to learn that an instructor would operate like that. It seems to me there was a lot wrong with that scenario in terms of handling and management.
Why did you not crossckeck instruments with the PNF?
Why did you not hand control over to him when it was obvious you had a pressure system failure on your side?
You should have anticipated erroneous airspeed indications after a pressure system failure even if you hadn't decided what exactly had failed so a stall warning too should not have been unexpected, for that to come as a surprise really startles me, and why wasn't PNF handling by that time?
In any case why just cram on' a few extra degrees' of pitch with a windshear warning? Is that really the correct technique?
How did all this stack up against your SOPs I wonder, or was this before the days of SOPs?
Sure, for rookie pilots or low hours guys new on type this sort of thing needs briefing, demonstarting and then practicing. An established line pilot should be able to cope with this as a minor irritation during recurrent trainig unbriefed and unanticipated, but for an isntructor to find it hard makes me feel very uncomfortable indeed.
The startle factor is doubtless something that will be looked at much more closely in future, as failure to recognise a runaway trim or reduce power from TOGA thrust because of a stall warner and odd instrument indications shouldn't ever happen. Especially when the only topic of conversation in your crew room over the last few months must have been about nothing else...