This is doing the rounds.
STOL stands Short Takeoff and Landings normally but in this context we can only assume they mean restricted approaches with higher than normal approach gradients more than 3 degs and short runways due terrain in the approach sector.
Stabilized approaches have come from years and years of data analysis of landing accidents. They basically require you to be full configured, checks done and in side the target speed for landing which is +30 -0 of your Vref (speed 50ft over threshold) roll inside certain limits (this is slightly different with circling approaches which is a whole different level of risk compared to a normal approach)
The examiner thing is a international thing in some nations where your 6 monthly check is observed by a none qualified examiner on type. For example in the ME I was checked by a A340 examiner on the Jetstream 41 and he had never flown a turboprop in his life. It doesn't occur in the USA or EU. But this one seems to say the local examiners all have to be checked externally so the old boy networks can't let failures through. So ATR examiners in Toulouse would have to test all the local examiners.
The rest of it is to do with flight time limitations and is for trying to limit fatigue.
The stabilised approach stuff is pretty obvious due to them being under 500ft and not yet pointing at the runway.
The rest is things that they have picked up doing the initial operator check.
Quite what an augmented flight crew duty is I have no clue. An augmented crew is used in ultra long haul were you have relief pilots on board or even a complete second crew but that only kicks in on 10 hour plus flights (I think I have never done that sort of ops) and I can't really see how that could be a feature for ATR pilots that the plane can stay in the air a max of 5 hours.