The car sports typical camouflage for models under development, somewhat odd considering the earlier reveal of the concept. One key difference between what was seen at Paris and the model in the video is a big wing sitting on the back of the car. The wing approximates the shape of the P1 at the rear, so could possibly be retractable, although its height would argue otherwise.
As of this posting, McLaren had not specified an engine for the P1, although the testing footage certainly argues that the question has been settled. Most likely, the P1 uses a similar twin turbo 3.8-liter V-8 as the one in the current MP4-12C model. The current engine produces 616 horsepower, but may get a boost in the newer car.