1. Assuming a common above ohm resistance range a 2-8 amp draw would be the norm. Does it benefit one to use higher amperage batteries at lower amp draws? Does this extend battery life? Both longevity (cycles) and the vape time for each session (mah) extended?
Your first priority when choosing a vaping battery should be for an adequate amp rating (continuous discharge rate or CDR). Then, choose a battery with a higher capacity (mAh) from that list.
So, yes, in general, it does benefit using higher amp batteries at lower amp draws, and can extend the overall longivity of the battery because its not being drained at its highest current output continuously.
2. If there would be a catastrophic event in that 2-8 amp range will using a higher amp battery give one more time to address the situation before a final thermal runaway with less load on it?
This is the whole point of using the "continuous" discharge rating instead of the "pulse" discharge rating when choosing batteries. If you are pushing your batteries to their upper limits by relying on pulse discharge rates, you are instantly "over-specced" for those batteries. There's no safe headroom available should a short occur. Bad things can happen really quickly!
This reminds me of the guy at a Texas vape convention a couple of years back. He was watching a "cloud chasing" competetion, when the mod in his pocket got HOT really quickly. He had some trouble removing it, and when he finally managed to remove it, he tossed it on the floor. The thing exploded like a hand grenade, with pieces making holes in the ceiling and catching the carpet on fire. The guy disappeared from the scene immediately, so no one knows what mod or what batteries or what resistance he was using; but its obvious a hard short occured and caused the batteries to vent.
However, if you allow yourself some safe headroom by using the continuous discharge rating, it gives you more time to notice a problem and take charge of the situation to prevent a catastrophe. At least you'll have time to notice if your button or mod body gets hot, and you'll have time to remove the atomizer or battery, or remove the mod from your pocket and place it out of harm's way.
The continuous discharge rate is a battery industry specification standard, and allows choosing between battery brands and models more easily. There is no spec standard in the industry for the pulse discharge rating, as each manufacturer defines this spec individually, and you have to research if their pulse is for a millisecond or several seconds or anywhere in between, (if they publish it at all). Therefore, pulse ratings are totally useless for vapers, IMHO.
Battery Pulse Ratings Are Useless