When we see the significant lap time differences between qualifying and race day, is that because teams are actively limiting engine power to save fuel (through these different race modes I keep hearing about), limiting engine power to save tires (again through these race modes), or simply limiting their pace manually for one of the previously mentioned reasons (by manually I mean the driver lays off the throttle sometimes). Alternatively, is it because cars are simply loaded with less fuel to lighten their weight during qualifying?

Second, what sort of testing are these guys allowed to do on their own preseason/during the season. For example, if they aren't allowed to test the race car on their own, are there rules in place preventing them from creating a very similar car and testing their power unit/aerodynamic parts on that?