They were in the right mind and they were fully intending to fight each other. Plus based off that fight it sounded more like a sparring match.
Yes but they were both fighting to the best of their abilities and wanted to truly see who was better.
The REAL Green Arrow from the comics would have bodied CW Flash.
The REAL Deadshot would have bodied CW Flash
In character maybe, but not bloodlusted since they have nothing to get around his phasing.
I also want to add their sparring match that they were referring to was seasons ago. And CW Arrow isn't anywhere near as versatile as other street levelers or his comic counterpart.