I believe it quite possible, even probable, that even if Jessica had been rendered unconscious beforehand, the sheer pain of flames on 98% of her body would shock the CNS back into hyperdrive. It would be a whole different reaction than if her unconscious body was slipped underwater to drown or even manually suffocated. It makes me ill to think of it, but it somehow reminds me of the horror of watching my grandfather shoot the head off a chicken when I was 5. The horrific "running around headless" was explained to me as the central nervous system being on autopilot. Though my 5 year old brain didn't understand that then, it makes more sense to me now. The chicken's heart was still beating and there was still enough oxygen to keep certain functions alive.
Once JC was conscious again, I can only imagine how vehemently she might have tried to identify her killer/s and everything else she possibly could to insure their deserved fate. Of course, that assumes she was ever unconscious.
On identifying her at the scene: in a small town such as Courtland, people tend to be pretty familiar with who drives what kind of car. It's possible that any of the first responders recognized her car on first sight.
Also, have you ever noticed that license plate numbers and letters are raised or embossed from the level of the flat license plate? That is so the plate will be "readable" for identification purposes should the car burn and burn all the paint off the plate. The raised letters and numbers are still recognizable even though the plate is burnt crispy and all one charcoal color.
I have no problem believing she was readily identified very early on by legitimate, non-nefarious means.