Hi Paul,
I might have to split your question up:
If premarket high is a higher price than the high after the market open, which one is the "high of day"?
The high of day is the highest price after the market open. If premarket high is a higher price, it is still just "premarket high", NOT high of day.
Should I plot premarket high/low?
Yes, and better yet you can have DAS automatically plot those levels for you.
Right click a Chart > Study Config > select a PriceMarker indicator > Configure to display PreMktHigh and PreMktLow.
You can do the same thing for High of Day and Low of Day as well,
but make sure your make the line style different from daily levels
otherwise you might accidentally think that the high of day bounced off of a daily level when there isn't actually a resistance there etc...