The delay element timing should start at motor ignition as both the propellant and delay grain are ignited at the same time usually.
No, the portion of the delay grain that burns during the motor burn time is taken into account by the motor manufacturer but is not taken out of the delay time. Assuming that a delay is drilled correctly, drilling a delay to be an 8 second delay means that there should be 8 seconds of delay left
after the motor has finished burning, not that the eight seconds of delay time begins when the motor ignites.
The delay is built long enough to burn during the motor's high pressure phase and afterwards. During the high pressure phase, the delay burns at a relatively high rate, such as five times the rate after burnout.
To put that into numbers, a fourteen second delay in a motor that burns for two seconds, would burn 10/32" while the motor burns (5/32 inch per second times two seconds) and 14/32" after burnout (1/32 inch per second for 14 seconds), for a total of 24/32" or 3/4".
Of course the rate while the motor is burning is dependent on the pressure within the motor and very sensitive to igniter placement, chuffing (like Terry explained above), contamination, delay grain seal, etc. We've all seen delays that were too quick and we've all seen delays that take too long. There used to be a term "aerotech bonus delay". I discovered that as I became more experienced I had fewer of those.