The trail leg and lead leg drill off the side can allow bad habits to creep in. So we have always done all the drills the middle of the hurdle. I am not sure if it’s a waste of time but I am sure you can accomlish everything going over the middle of the hurdle.
Regarding the warm-up for a hurdle race, the same warm-up as done for sprinting with some additional static hurdle stretching, static trail leg rotation, five step hurdling over 4 H or so and couple of runs over 2 hurdles and then race.