Close, but not quite. If the battery SOC is low then the power demand is a combination of go pedal and battery demands. In general you are right though: ICE power is not set according to maximum ICE efficiency. It just seems that way
To this end it is always important to keep an eye on SOC use. If you are draining the SOC down to a point at which the ICE will be forced to recharge it to a large extent then you are not driving in the most efficient manner. Conversion losses suck.
Yep. And sometimes you get a double-whammy for your troubles, because the low SOC pushes the ICE to operate in an inefficient band until the battery is happy again.