CS - Nothing wrong with "asking endless questions".
What we are talking about here is point (4) on the Punk666 list "A/c unsafe to fly". Manufacturers put this in to cover product liability claims...it enables them to look at an incorrect RTO decision after the event and blame the pilot.
To be fair it is not realistic for Boeing or anyone else to provide an exhaustive list because the crux of the matter (as Capt Solipist pointed out) is that it is situational.
Yes there are a lot of clear rights and wrongs....obvious gos or no gos...but there is also a lot of grey in the "unsafe to fly" catch all.
One key element (and there are many) is runway length...if you are taking off from a 3000 metre runway you will typically reach 80 knots in the first 10% -the rate of acceleration slows rapidly as you approach 100 knots.
My view on the scenarios you mention...
(i) Engine overheat - There are people who show relatively little concern for this warning. Bad move - the core section overheat warning triggers at 343 degrees ....this is serious heat (core fire warning is not much higher at 454).
I had to abandoned a take off at Belfast Aldergrove due to an overheat warning...the rate of increase of turbine temp was also seen to be accelerating rapidly (another variable...single or multiple indications). Cause failure of a pipe weld and mass ejection of core air into the nacelle. Even though the thrust levers were retarded immediately the engine temeprature continued to rise during the deceleration and it cooked itself. Senior engineers subsequently advised that if take off thrust had been maintained then in less than a minute the engine would have failed catastrophically.
(ii) Take off config. As has already been said this warning should have gone off as soon as the thrust levers were advanced. If vibration has just taken the the trim slightly out of the take off range no big deal. If the flaps have retracted from 5 to zero and you rotate at flap 5 speeds the aircraft will stall as soon as it leaves ground effect.
(iii) Door open...again it has been said this is not an unsafe to fly condition which would cause a high energy reject on a runway limited take off. If on 3000m strip with 15 knot headwind a door fully opens at 90 knots airspeed....you will feel it on your ears and there will be a yaw. Although in a court of law you may successfully defend continuing the take off (re. point 4) this would be a poor decision....not least because the groundspeed (which is the important number) was only 75 knots.